(From Hutton's Mathematics.)

No.

Square.

Cube.

Sq. Root.

CubeRoot.

1

1

1

1.0000000

1.000000

2

4

8

1.4142136

1.259921

3

9

27

1.7320508

1.442250

4

16

64

2.0000000

1.537401

5

25

125

2.2360680

1.709976

6

36

216

2.4494897

1.817121

7

49

343

2.6457513

1.912931

8

64

512

2.8284271

2.000300

9

81

729

3.0000000

2.080084

10

100

1000

3.1622777

2.154435

11

121

1331

3.3166243

2.223930

12

144

1728

3.4641016

2.239429

13

169

2197

3.6055513

2351335

14

196

2744

3.7416574

2.410142

15

225

3375

3.8729833

2.466212

16

256

4096

4. 0000000

2.519842

17

239

4913

41231056

2.571282

18

324

5332

4.2426407

2.620741

19

361

6859

4.3588989

2.663402

20

400

8000

4.4721360

2.714418

21

441

9261

4.5825757

2.758924

22

484

10643

4.6904158

2.802039

23

529

12167

4.7953315

2.843367

24

576

13324

4.8989795

2.884499

25

625

15625

5.0000000

2.924018

26

676

17576

5.0990195

2.962496

27

729

19683

5.1961524

3.000000

28

784

21952

5 .2915028

3.036589

29

841

24389

5.3851648

3.072317

30

900

27000

5.4772256

3.107232

31

961

29791

55677644

3.141331

32

1024

32763

5.6568542

3.174802

33

1089

35937

5 7445626

3.207534

34

1156

39304

5.8399519

3.239612

35

1225

42875

5.9160798

3.271066

36

1296

46656

6 0000000

3.391927

37

1369

50653

6.0327625

3.332222

38

1444

54872

61644140

3.361975

39

1521

59319

6.2449980

3.391211

40

1600

64000

6.3245553

3.419952

41

1681

68921

6.4031242

3. 448217

42

1764

74038

6.4807407

3.476027

43

1849

79507

6.5574385

3.503398

44

1936

85184

6 6332496

3533348

45

2025

91125

6.7082039

3.556893

46

2116

97336

6.7823300

3.533348

47

2209

103323

6.8556546

3.608826

48

2304

110592

6.9232032

3.634241

49

2401

117649

7.0090030

3.659336

50

2500

125000

70710678

3.634031

51

2601

132651

7.1414284

3.708433

52

2704

140608

7.2111026

3.732511

53

2809

148877

7.2301099

3.756286

54

2916

157461

7.3484692

3.779763

55

3025

166375

7.4161985

3.302952

56

3136

175616

7.4833148

3.825862

57

3219

185193

7.5493344

3.343501

58

3364

195112

7.6157731

3.870877

59

3481

205379

7.6311457

3.892996

60

3600

216000

7.7459667

3.914868

61

3721

226981

7.8102497

3.936497

62

3344

233328

7.8740079

3..957891

63

3969

250047

7.9372539

3.979057

64

4096

262144

8. 0000000

4.000000

65

4225

274625

8.0622577

4.029726

66

4356

237496

8.1240384

4041240

67

4489

300763

8.1853523

4061548

No.

Square.

Cube.

Sq. Root.

CubeRoot.

68

4624

314432

8.2462113

4.081655

69

4761

328509

8.3066239

4 101566

70

4900

343000

8.3666003

4.121285

71

5041

357911

8.4261498

4.140818

72

5184

373248

8.4852814

4.160168

73

5329

389317

8.5440037

4.179339

74

5476

405224

8.6023253

4.193336

75

5625

421875

8.6602540

4 217163

76

5776

433976

8.7177979

4 235324

77

5929

456533

8.7749644

4.254321

78

6084

474552

8.8317609

4.272659

79

6241

493039

8.8881944

4.290840

83

6403

512000

8.9442719

4.308869

81

6561

531441

9.0000000

4.326749

82

6724

551368

9.0553851

4.344481

83

6889

571787

9.1104336

4.362071

84

7056

592704

9.1651514

4.379519

85

7225

614125

9.2195445

4.396830

86

7396

636056

9.2736185

4.414005

87

7569

653503

9.3273791

4.431048

88

7744

681472

9.3808315

4.447960

89

7921

704969

9.4339811

4.464745

90

8100

729300

9.4368330

4.481405

91

8281

753571

9.5393929

4.497941

92

8164

778688

9.5916630

4.514357

93

8649

804357

9 6436508

4.530655

94

8836

830584

9.6953597

4.516836

95

9025

857375

9.7467943

4.560903

96

9216

884736

9.7979590

4.578857

97

9409

912673

9.8483578

4.591701

98

9604

941192

9.8994949

4.610436

99

9301

970299

9.9498744

4.626065

100

10000

1000000

10.0000000

4 641589

101

10201

1030301

10.0498756

4.657009

102

10404

1061208

100995049

4.672329

103

10609

1092727

10.1488916

4.687548

104

10816

1124864

10.1980390

4.702669

105

11025

1157625

10.2469508

4.717694

106

11236

1191016

10.2956301

4.732623

107

11449

1225043

10.3440804

4.747459

108

11664

1259712

10.3923348

4.762203

109

11831

1295029

10.4403365

4.776356

110

12100

1331000

10.4880885

4.791420

111

12321

1367631

10.5356533

4.805895

112

12544

1404928

10.5330052

4.820284

113

12769

1442897

10.6301458

4.334588

114

12996

1481544

10.6770783

4.348808

115

13225

1520875

10.7238053

4.862944

116

13456

1560896

10.7703236

4.876999

117

13689

1601613

10.8168538

4.890973

118

13924

1643032

10.8627805

4.904868

119

14161

1685159

10.9087121

4.913685

120

14400

1728000

10.9541512

4932424

121

14641

1771561

ll.0000000

4.946087

122

14884

1815848

11.0453610

4.959676

123

15129

1860867

11.0905365

4.973190

124

15376

1906624

11.1355287

4.986631

125

15625

1953125

11.1803399

5.000000

126

15876

2000376

11.2249722

5.013298

127

16129

2048383

11.2694277

5.026526

128

16384

2097152

11.3137085

5 039684

129

16641

2146689

11.357378167

5.052774

130

16900

2197000

11.4017543

5 065797

131

17161

2248091

11.4455231

5.078753

132

17424

2299963

11.4891253

5.091643

133

17689

2352637

11.5325626

5.104469

134

17956

2406104

11.5758369

5.117230

No.

Square.

Cube.

Sq. Root.

CubeRoot.

135

18225

2460375

11.6189500

5.129928

136

18496

2515456

11.6619038

5.142563

137

18769

2571353

11.7046999

5.155137

138

19044

2628072

11.7473101

5.167649

139

19321

2685619

11.7898261

5.180101

140

19600

2744000

11.8321596

5.192494

141

19881

2803221

11.8743422

5.204828

142

20164

2863283

11.9163753

5.217103

143

20449

2924207

ll.9582607

5.229321

144

20736

2985984

12.0000000

5.241483

145

21025

3048625

12.0415946

5.253588

146

21316

3112136

12.0830460

5.265637

147

21609

3176523

12.1243557

5.277632

148

21904

3241792

12.1655251

5.289572

149

22201

3307949

12.2065556

5.301459

150

22500

3375000

12.2174487

5.313293

151

22801

3442951

12.2882057

5.325074

152

23104

3511808

12.3288280

5.336803

153

23409

3531577

12.3693169

5.348481

154

23716

3652264

12.4096736

5.360108

155

24025

3723375

12.4498996

5.371685

156

21336

3796416

12.4899960

5.333213

157

24649

3869893

12.5299641

5.394691

158

24964

3941312

12.5698051

5.406120

159

25281

4019679

12.6095202

5.417501

160

25600

4096000

12.6191106

5.428835

161

25921

4173281

12.6885775

5.440122

162

26214

4251528

12.7279221

5.451362

163

26569

4330747

12.7671453

5.462556

164

26896

4410944

12.8062485

5.473704

165

27225

4492125

12.8452326

5.484807

166

27556

4574296

12.8840987

5.495865

167

27889

4657463

12.9228480

5.506878

168

28224

4741632

12.9614814

5.517848

169

28561

4826809

13 0000000

5.528775

170

28900

4913000

13.0384048

5.539658

171

29241

5000211

13.0766968

5.550499

172

29584

5088448

13.1148770

5.561298

173

29929

5177717

13.1529464

5.572055

174

30276

5268024

13.1909060

5.532770

175

30625

5359375

13.2287565

5.593145

176

30976

5151776

13.2664992

5.604079

177

31329

5515233

13.3041317

5.614672

178

31684

5639752

13.3416641

5.625226

179

32041

5735339

13.3790882

5.635741

180

32400

5832000

13.4164079

5.646216

181

32761

5929741

13.4536240

5.656653

182

38124

6028568

13.4907376

5.667051

183

33489

6128487

13.5277493

5.677411

181

33836

6229504

13.5646600

5.687734

185

34225

6331625

13.6014705

5.698019

186

34596

6434856

13.6381817

5.703267

187

34969

6539203

13.6747943

5.718179

183

35344

6644672

13.7113092

5.728654

189

35721

6751269

13.7477271

5.738794

190

36100

6859000

13.7840488

5.748397

191

36481

6967871

13.8202750

5.758965

192

36864

7077888

13.8564065

5.768998

193

37249

7189057

13.8924440

5.778996

191

37636

7301384

13.9283383

5.788960

195

38025

7414875

13.9642400

5.798890

196

38416

7529536

14.0000000

5.808786

197

38809

7615373

14.0356688

5.818648

198

39204

7762392

14.0712473

5.828477

199

39601

7880599

14.1067360

5.838272

200

10000

8000000

14.1421356

5.848035

201

40401

8120601

14.1774469

5.857766

No.

Square.

Cube.

Sq. Root.

CubeRoot

202

40804

8242408

14.2126704

5.867164

203

41209

8365427

14.2478068

5.877131

204

41616

8489664

14.2328569

5.886765

205

42025

8615123

14.3178211

5.896368

206

42436

8741816

14.3527001

5.905941

207

42849

8869743

14.3874946

5.915482

208

43264

8998912

14.4222051

5.924992

209

43681

9129329

14.4568323

5.931473

210

44100

9261000

14.4913767

5 943922

211

44521

9393931

14.5258390

5.953342

212

44944

9528128

14.5602198

5.962732

213

45369

9663597

14.5945195

5.972093

214

45796

9800344

14.6287388

5.931421

215

46225

9938375

14.6624783

5.990726

216

46656

10077696

14.6969385

6.000000

217

47089

10218313

14.7309199

6009245

218

47524

10360232

14.7648231

6.018462

219

47961

10503459

14.7986486

6.027650

220

48400

10648000

14.8323970

6.036811

221

48841

10793861

14.8660687

6.045943

222

49284

10941048

14.8996644

6.055049

223

49729

11039567

14.9331815

6.064127

224

50176

11239424

14.9666295

6.073178

225

50625

11390625

15.0000000

6.082202

226

51076

11543176

15.0332964

0.091199

227

51529

11697083

15.0665192

6.100170

228

51984

1185235.2

15.0996689

6.109115

229

52441

12008939

15.1327460

6.118033

230

52900

12167000

15.1657509

6.126926

231

53361

12326391

15.1986842

6.135792

232

53824

12487168

15.2315462

6.144634

233

54289

12619337

15.2643375

6.153449

234

54756

12812904

15.2970585

6.162240

235

55225

12977875

15.3297097

6.171006

236

55696

13144256

15 3622915

6.179747

237

56169

13312053

15.3943043

6.183463

233

56644

13181272

15.4272486

6.197154

239

57121

13651919

15.4596248

6.205822

240

57600

13324000

15.4919334

6.214465

241

58081

13977521

15.5211717

6.223084

242

58564

14172488

15.5563192

6.231680

243

59049

14348907

15.5884573

6.240251

244

59536

14526784

15.6204994

6.248800

245

60025

14706125

15.6524758

6.257325

246

60516

14886936

15.6343371

6.265827

247

61009

15059223

15.7162335

6.274305

248

61504

15252992

15.7480157

6.282701

249

62001

15438249

15.7797333

6.291195

250

62500

15625000

15.8113883

6.299605

251

63001

15813251

15.8429795

6.307994

252

63504

16003008

15.8745079

6.316360

253

64009

16191277

15.9059737

6.321701

254

64516

16387061

15.9373775

6.333026

255

65025

16581375

15.9687194

6.311326

256

65536

16777216

16.0000000

6.349604

257

65049

16974593

16.0312195

6.357861

253

66564

17173512

16.0623731

6.366097

259

67081

17373979

16.0934769

6.374311

260

67600

17576000

16.1215155

6.382504

261

68121

17779581

16.1554944

6.390676

262

63644

17981723

16.1861141

6.398828

263

69169

18191447

16.2172747

6.406958

264

69696

18399744

16.2180768

6.415969

265

70225

18609625

16.2788206

6.423158

265

70756

18821096

16.3095064

6.431228.

267

71289

19034163

163.101316

6.439277

268

71824

19248832

16.3707055

6.447306

No

Square.

Cube.

Sq. Root.

CubeRoot.

269

72361

19465109

16.4012195

6.455315

270

72900

19683000

164316767

6.463304

271

73441

19902511

16.4620776

6.471274

272

73984

20123648

16.4924225

6.479224

273

74529

20346417

16.5227116

6.487154

274

75076

20570824

16.5529454

6.495065

275

75625

20796875

16.5331240

6.502957

276

76176

21024576

16.6132477

6.510830

277

76729

21253933

16.6433170

6.518684

278

77234

21484952

16.6733320

6.526519

279

77811

21717639

16.7032931

6534335

290

78400

21952000

16.7332005

6.542133

281

78961

22188041

16.7630546

6.549912

282

79524

22425768

16.7923556

6.557672

233

80089

22665187

16.8226033

6 565414

284

80656

22906304

16.8522995

6.573139

235

81225

23149125

16.8819430

6.530844

286

81796

23393656

16.9115345

6538532

287

82369

23639903

16.9410743

6.596202

283

82944

23387872

16.9705627

6.603854

239

83521

24137569

17.0000000

6.611489

290

84100

24389000

17.0293864

6.619106

291

84681

24642171

170537221

6.626705

292

85264

24897088

17.0880075

6.634237

293

85849

25153757

17.1172428

6.641852

294

86136

25412184

171464232

6.649400

295

87025

25672375

171755640

6.656930

296

87616

25934336

17.2046505

6.664444

297

88209

26198073

17.2336879

6.671940

298

88804

26463592

17.2626765

6.679420

299

89401

26730899

17.2916165

6.686883

300

90000

27000000

17.3205081

6.694329

301

90601

27270901

17.3493516

6.701759

302

91204

27543603

17.3781472

6.709173

303

91809

27818127

17.4068952

6.716570

304

92416

28094464

17.4355958

6.723951

305

93025

28372625

17.4642492

6.731316

306

93636

23652616

17.4928557

6.738664

307

94249

28934443

175214155

6.745997

308

94864

29218112

17.5499288

6.753313

309

95481

29503629

17.5783958

6.760614

310

96100

29791000

17.6068169

6.767899

311

96721

30080231

17.6351921

6.775169

312

97344

30371328

17.6635217

6.782423

313

97969

33664297

17.6918060

6.789661

311

98596

30959144

17.7200451

6.796884

315

99225

31255875

17.7482393

6.804092

316

99856

31554496

| 17.7763888

6.811285

317

100489

31855013

17.8044938

6.818462

318

101124

32157432

17.8325545

6.825624

3l9

101761

32461759

17.8605711

6.832771

320

102400

32768000

17.8835433

6.839904

321

103041

33076161

17.9164729

6.847021

322

103684

33386248

179443534

6 854124

323

104329

33698267

17.9722008

6.861212

324

104976

34012224

18.0000000

6.868285

325

105625

34328125

18.0277564

6.875344

326

106276

34645976

18.0554701

6.882339

327

106929

34965783

180831413

6.889419

328

107584

35287552

18.1107703

6.896435

329

108241

35611289

18.1383571

6903436

330

108900

35937000

18.1659021

6.910423

331

109561

36264691

18.1934054

6.917396

332

110224

36594368

18.2208672

6.924356

332

110889

36926037

18.2482876

6.931301

331

111556

37259704

18.2756669

6.938232

333

112225

37595375

18.3030052

6.945150

No.

Square.

Cube.

Sq Root.

CubeRoot.

336

112896

37933056

18.3303028

6.952053

337

113569

38272753

18.3575598

6.958943

333

114244

38614472

18.3847763

6.965820

339

114921

38908219

18.4119526

6.972683

340

115600

39304000

18.4390889

6.979532

341

116281

39651821

18 4661853

6.986368

342

116964

40001638

18.4932420

6.993191

343

117649

40353607

18.5202592

7.000000

344

118336

40707584

18.5472370

7.006796

345

119025

41063625

18.5741756

7.013579

346

119716

41421736

18.6010752

7.020349

347

120409

41781923

18.6279360

7.027106

343

121104

42144192

18.6547581

7.033850

349

121801

42508549

18.6815417

7.040581

350

122500

42875300

18.7082869

7.047299

351

123201

43243551

18.7349940

7.054004

352

123904

43614208

18.7616630

7.060697

353

124609

43985977

18.7882942

7.067377

354

125316

44361864

18.8148877

7.074044

355

126025

44738875

18.8414437

7.080699

356

126736

45118016

18.8679623

7.087341

357

127449

45499293

18.8944436

7093971

358

128164

45882712

18.9208879

7.100588

359

128881

46268279

18.9472953

7107194

360

129600

46656000

18.9736660

7.113787

361

130321

47045381

19.0000000

7.120367

352

131044

47437928

19.0262976

7.126936

363

131769

47832147

19.0525589

7.133492

364

132496

48228544

19.0787840

7.140037

365

133225

48627125

19.1049732

7.146569

366

133956

49027396

19.1311265

7.153090

367

134689

49430863

19.1572441

7.159599

368

135424

49835032

19.1833261

7.166096

369

136161

59243409

19.2093727

7.172581

370

136900

50653300

19.2353841

7.179054

371

137641

51064811

19.2613603

7185516

372

138384

51478848

19.2873015

7.191966

373

139129

51895117

19.3132079

7.198405

374

139876

52313624

19.3390796

7.204832

375

140625

52734375

19.3649167

7.211248

376

141376

53157376

19.3907194

7.217652

377

142129

53582633

19.4164878

7.224045

378

142884

54010152

19.4422221

7.233427

379

143641

54439939

19.4679223

7.236797

380

144400

54872000

19.4935887

7.243156

381

145161

55306341

195192213

7.249504

382

145924

55742968

19.5448203

7.255841

383

146689

56181887

19.5703858

7.262167

384

147456

56623104

19.5959179

7.268482

385

148225

57066625

19.6214169

7.274786

386

148996

57512456

19.6468327

7.231079

387

149769

57960603

19.6723156

7.287362

388

150544

58411072

19.6977156

7.293633

389

151321

53863869

19.7230829

7.299894

390

152100

59319000

19.7484177

7.306144

391

152881

59776471

19.7737199

7.312383

392

153664

60236288

19.7989899

7.318611

393

154449

60693457

19.8242276

7.324829

394

155236

61162984

19.8494332

7.331037

395

156025

61629875

19.8746069

7.337234

396

156816

62099136

19.8997487

7.343420

397

157609

62570773

19.9248538

7.349597

398

158404

63044792

19.9499373

7.355762

339

159201

63521199

19.9749844

7.361918

400

160000

64000000

20.0000000

7.363063

401

160801

64481201

20.0249344

7.374198

402

161604

64964808

20.0499377

7.330323

No.

Square.

Cube.

Sq. Root

CubeRoot.

403

162409

65450827

200748599

7.336437

404

163216

65939264

200997512

7.392542

405

164025

66430125

201246118

7.398636

406

164836

66923416

20.1494417

7.404721

407

165849

67419143

20.1742410

7.410795

408

166464

67917312

20.1990099

7.416859

409

167281

68417929

20.2237484

7.422914

410

168100

68921000

20.2484567

7.428959

411

168921

69426431

20.2731349

7434994

412

169744

69934423

20.2977831

7.441019

413

170569

70444997

20.3224014

7.447034

414

171396

70957944

20.3469899

7.453040

415

172225

71473375

20.3715488

7.459035

410

173056

71991296

20.3960781

7.465022

417

173889

72511713

20.4205779

7.470999

418

174724

73034632

20.4450483

7.476966

419

175561

73560059

20.4694895

7.482924

420

176400

74088000

20.4939015

7.488872

421

177241

74618461

20.5182845

7.494811

422

178084

75151448

20.5426386

7.500741

423

178929

75686967

20.5669638

7.506661

424

179776

76225024

20.5912603

7.512571

425

180625

76765625

20.6155281

7.518473

426

181476

77308776

20.6397674

7.524365

427

182329

77854483

20.6639783

7.530248

428

183184

78402752

20.6881609

7.535122

429

184041

78953589

20.7123152

7.541987

430

184900

79507000

20.7364414

7.547842

431

185761

80062991

20.7605395

7.553689

432

186624

80621568

20.7846097

7.559526

433

187489

81182737

20.8086520

7.565355

434

188356

81746504

20.8326667

7.571174

435

189225

82312875

20.8566536

7.576985

436

190096

82881856

20.8806130

7.582786

437

190969

83453453

20.9045450

7.588579

438

191844

84027672

20.9284495

7.594363

439

192721

84604519

20.9523268

7.600138

440

193600

85184000

20.9761770

7.605905

441

194481

85766121

21.0000000

7.611663

442

195364

86350888

21.0237960

7.617412

443

196219

86938307

21.0475652

7.623152

444

197136

87528384

21.0713075

7.628884

445

198025

88121125

21.0950231

7.634607

446

198916

88716536

21.1187121

7.610321

447

199809

89314623

21.1423745

7.646027

448

200704

89915392

21.1660105

7.661725

449

201601

90518849

21.1896201

7.657414

450

202500

91125000

21.2132034

7.663094

451

203401

91733851

21.2367606

7.668766

452

204304

92345408

21.2602916

7.674430

453

205209

92959677

21.2837967

7.680086

454

206116

93576664

21.3072758

7.685733

455

207025

94196375

21.3307290

7691372

456

207936

94818816

21.3541565

7.697002

457

208849

95443993

21.3775583

7.702625

458

209764

96071912

21.4009346

7.708239

459

210681

96702579

21.4242853

7.713845

460

211600

97336000

21.4476106

7.719113

461

212521

97972181

21.4709106

7.725032

462

213414

98511128

21.4941853

7.730614

463

214369

99252847

21.5174318

7.736188

464

215296

99897344

21.5406592

7.741753

465

216225

100511625

21.56385871

7.747311

466

217156

101194696

21.5870331

7.752861

467

218089

101847563

31.6101828

7.758402

468

219024

102503232

21.6333077

7.763936

469

219961

103161709

21.6564078

7.769162

No.

Square.

Cube.

Sq. Root.

CubeRoot.

470

220900

103823000

21.6794834

7.774980

471

221841

104487111

21.7025344

7.780190

472

222784

105154048

21.7255610

7.785993

473

223729

105823817

21.7485632

7.791487

474

224676

106496424

21.7715411

7.796974

475

225625

107171875

21.7944947

7.802454

476

226576

107850176

21.8174242

7.807925

477

227529

108531333

21.8403297

7.813389

478

223484

109215352

21.8632111

7.818846

479

229441

109902239

21.8860686

7.824294

430

230400

110592000

21.9089023

7.829735

431

231361

111284641

21.9317122

7.835169

482

232324

111930163

21.9544934

7.840595

483

233289

112678537

21.9772610

7846013

434

234256

113379904

22.0000000

7.851424

485

235225

114084125

22.0227155

7.856828

486

236196

114791256

22.0454077

7.862224

487

237169

115501303

22.0680765

7.867613

488

238144

116214272

22.0907220

7.872994

439

239121

116930169

22.1133444

7.878368

490

240100

117649000

22.1359436

7.883735

491

241031

118370771

22.1585198

7.889095

492

212064

119095488

22.1810739

7.894447

493

213049

119823157

22.2636033

7.899792

494

244036

120553784

22.2251108

7.905129

495

245025

121287375

22.2485955

7.910460

496

246016

122023936

22.2710575

7.915783

497

247009

122763473

22.2934968

7.921099

498

248004

123595992

22.3459135

7.926403

499

249001

124251499

22.3383079

7.931710

500

250000

125000000

22.360o798

7.937005

501

251001

125751501

22.3330293

7.942293

502

252004

126506008

22.4053565

7.947574

503

253009

127263527

22.4276615

7.952848

504

254016

128024061

22.4499443

7.958114

505

255025

128787625

22.4722051

7.963374

506

256036

129554216

22.4944438

7.968627

507

257049

130323343

22 5166605

7.973873

508

258064

131096512

22.5388553

7.979112

509

259081

131872229

22.5510283

7.984344

510

260100

132651000

22.5331796

7.989570

511

261121

133432831

22.6053091

7.994788

512

262144

134217723

22.6274170

8.000000

513

263169

135005697

22.6495933

8.0052000

514

264196

135796744

22.6715581

8.010403

515

265225

136590875

22.6936114

8.015595

516

266256

137388096

22.7156334'

8.020779

517

267289

138188413

22.7376340

8.025957

518

268324

138991832

22.7596134

8.031129

519

269351

139798359

22.7815715

8.036293

520

270400

140608000

22.8035085

8.041451

521

271441

141420761

22.8254244

8.046603

522

272484

142236618

22.8473193

8.051748

523

273529

143055667

22.8691933

8.056886

524

274576

113877824

22.8910463

8.062018

525

275625

144703125

22.9128785

8.067143

526

276676

145531576

22.9346899

8.072262

527

277729

146363183

22.9554896

8.077374

528

278784

147197952

22.9782506

8.082480

529

279841

148035889

23.0000000

8.087579

530

280900

148877000

23.0217289

8.092672

531

281961

149721291

23.0434372

8.097759

532

283024

150558763

23.0651252

8.102839

533

284089

151419437

23.0867928

8.107913

531

285156

152273304

23.1084400

8.112980

535

286225

153130375

23.1300670

8118041

536

287206

153990656

23.1516738

8.123090.

No.

Square.

Cube.

Sq. Root.

CubeRoot.

537

233369

154854153

23.1732605

8.123145

533

239444

155720872

23.1948270

8.133187

539

290521

156590819;

23.2163735

8133223

540

291600

157464030;

23.2379001

8.143253

541

292681

158340421

23.2594067

8.148276

542

293764

159220088

23.2808935

8153294

543

294849

160103007

23.3023604

8.158305

544

295936

160939184'

23.3233076

8163310

545

297025

161878625

23.3452351

8.168309

546

298116

162771336

23.3665429

8.173302

547

299209

163667323

23.3880311

8.178239

548

300304

164566592

23.4093998

8.183269

549

301401

165469149

23.4307490

8.188244

550

302500

166375000

23.4520788

8.193213

551

303601

167284151

23.4733392

8.198175

552

334704

168196608

23.4946802

8.203132

553

3055809

169112377

23.5159520

8.203082

554

306916

170031464

23.5372046

8.213027

555

308025

170953375

23.5534333

8.217966

556

309136

171879616

23.5796522

8.222898

557

310249

172308693

236003474

8.227825

558

311364

173741112

236220236

8.232746

559

312431

174676879

23.6431808

8.237661

560

313600

175616000

23.6 543191

8.242571

561

314721

176558481

23.6854386

8.247474

562

315344

177034328

237065392

8.252371

563

316969

178453547

23.7276210

8.257263

564

318096

179406144

23.7486342

8.262149

565

319225

180362125

23.7697285

8.267029

566

320356

181321496

23.7907515!

8.271904

567

321489

182284263

23.8117618

8.276773

568

322624

183250432

23.8327506

8.281635

569

323761

184220009

23.8537209

8.236493

570

324900

185193000

23.8746728!

8.291344

571

326041

186169411

23.8956063

8.296190

572

327184

187149248

23.9165215

8.331030

573

328329

183132517

23.9374184,

8.335865

574

329476

189119224

23.9582971

8.310694

575

330625

190109375

23.9791576

8.315517

576

331776

191102976

24.0000000

8.320335

577

332929

192103033

24.0208243

8.325147!

578

334034

193100552

24.0416306

8.329954

579

335241

194104539

24.0624183

8.334755

580

336400

195112000

24.0331891

8.339551

581

337561

196122941

24.1039416

8.344341

532

338724

197137368

24.1246762

8.349126

583

339889

193155287

24.1453929

8.353905

534

341056

199176704

24.1660919

8.353678

535

342225

200201625

24.1867732

8 353417

586

343395

201230056

242074359

8.353209

587

344569

202262003

24.2230829

8.372967

588

345744

203297472

24.2487113

8.377719

589

346921

204336169

24.2593222

8.332465

590

343100

205379000

24.2899156

8.337206

591

349281

206425071

24.3104916

8.391942

592

350464

207474688

24.3310501

8.336673

5931

351649

208527857

24.3515913

8.401398

594

352836

209584584

24.3721152

8.406118

595

354025

210644875

24.3326218

8.410333

596

355216

211708736

24.4131112

8.415542

597

356109

212776173

24.4335834

8.420246

598

357604

213847192

214540385

8.424045

599

353801

214921799

21.4744765

8.429633

600

360000

216000000

24.4948974

8.434327

601

361201

217081801

24.5153013

8.439010

602

362404

218167208

24.5356883

8.443688

603

363609

219256227

24.5560583

8.418360

No.

Square.

Cube.

Sq.Root

Cub Root.

604

34816

220348864

24.5764115

8.453026

605

3.6025

221445125

24.5967478

8.457691

606

367236

222545016

24.6170673

8.462348

607

368449

223648543

24.6373700

8.467000

608

369664

224755712

24.6576560

8.471647

609

370881

225866529

24.6779254

8.476239

610

372100

226981000

24.6981781

8.480926

611

373321

228099131

24.7184142

8.485558

612

374554

229220928

24.7386338

8.490185

613

375769

230346397

24.7588358

8.494806

611

376996

231475544

24.7790234

8.499423

615

378225

232608375

24.7991935

8.504035

616

379456

233744896

24.8193473

8.508642

617

380689

234885113

24.8394347

8.513243

618

381924

236029032

24.8596058

8.517840

619

383161

237176659

24.8797106

8.522432

620

381400

238328000

24.8997992

8.527019

621

385641

239483061

24.9198716

8.531601

622

386884

240641848

24.9399278

8.535178

623

386129

241804367

24.9591679

8.540750

624

389376

242970624

24.9799920

8.545317

625

390625

244140625

25.0000000

8.549880

626

391876

245314376

25.0199923

8.551437

627

393129

246491833

25.0399681

8.558990

623

394381

247673152

25.0599282

8.563538

629

395641

248853189

25.0798724

8.568081

630

396900

250047000

25.0998008

8.572619

631

398161

251239591

25.1197134

8 577152

632

309424

252435968

25.1396102

8.581681

633

400689

253636137

25.1591913

8.586205

634

401956

254810104

25.1793566

8.590724

635

403225

256047875

25.1992063

8.595233

636

404496

257259456

25.2190404

8.599748

637

405769

258174853

25.2388539

8.604252

638

407044

259694072

25.2536619

8.608753

639

408321

260917119

25.2784493

8.613248

640

409600

262144000

25.2932213

8.617739

641

410881

263374721

25.3179778

8.622225

642

412164

264609288

25.3377189

8.626706

643

413419

265847707

25.3574447

8.631183

644

414736

267089984

25.3771551

8.635655

645

416025

268336125

25.3968532

8.640123

646

417316

269586136

25.4165301

8.644585

647

418509

270810023

25.4351947

8.649044

648

419904

272097792

25.4558441

8.653497

649

421201

273359449

25.4751784

8.657946

650

422500

274625000

25.49509776

8.662391

651

423801

275894451

25.5147016

8.666331

652

425104

277167808

25.5342907

8.671266

653

426409

278145077

25.5533647

8 675697

654

427716

279726264

25.5734237

8.680124

655

429025

281011375

25.5929678

8.684546

656

43336

282300416

25.6124969

8.688963

657

431649

i 283593393

25.6320112

8693376

658

432964

284890312

25.6515107

8.697781

659

431281

286191179

25.6709953

8.702188

660

435600

287496000

25.6904652

8706538

661

436921

288804781

25.7099203

8.710983

662

438244

290117523

25.7293607

8715373

663

439569

291434247

25.7487854

8.719760

664

440896

292751944

25.7681975

8 721141

665

442225

294079625

25.7875939

8.728518

666

443556

295408296

25.8069758

8732392

667

444889

296740963

25.8263431

8737260

668

446224

298077632

25.8456960

8741625

669

447561

299418309

25.8650343

8715985

670

448900

300763000

25.8843582

8.753340

No

Square.

Cube.

Sq. Root.

CubeRoot.

671

450241

302111711

25.9036677

8.754691

672

451584

303464448

25.9229628

8.759038

673

452929

304821217

25.9422435

8.763381

674

454276

306182024

25.9615100

8.767719

675

455625

307546875

25.9807621

8.772053

676

456976

308915776

26.0000000

8.776383

677

458329

310288733

26.0192237

8.780708

678

459684

311665752

260384331

8.785030

679

461041

313046839

26.0576284

8.789347

680

462406

314432600

26.0768096

8.793659

681

463761

315821241

26.0959767

8.797968

682

460124

317214568

26.1151297

8.802272

683

466489

318611987

26.1342687

8.806572

684

467856

320013504

26.1533937

8.810868

685

469225

321419125

26.1725047

8.815160

686

470596

322828856

26.1916017

8.819447

687

471969

324242703

26.2106848

8.823731

688

473344

325660672

26.2297541

8.828010

689

474721

327082769

26.2488095

8.832285

690

476106

328509660

26.678511

8.836556

691

477481

329939371

26.868789

8.840823

692

478861

331373888

26.3058929

8.845085

693

480249

33*2812557

26.3248932

8.84*344

694

181636

334255384

26.3438797

8.853598

695

483025

335702375

26.3628527

8.857849

696

481416

337153536

26.3818119

8.862095

697

485809

338608873

26.4007576

8.866337

698

487204

340068392

26.4196896

8.870576

699

488601

341532099

26.4386081

8.874810

700

490000

343000006

26.4575131

8.879040

701

491401

344472101

26.4764046

8.883266

702

492804

345948408

26.4952826

8.887488

703

494209

347428927

26.5141472

8.891706

704

495616

348913661

26.5329983

8.895920

705

497025

350402625

26.5518361

8.900130

706

498436

351895816

26 5766605

8.904337

707

499849

353393243

26.5894716

8.968539

708

501264

354894912

26 6082694

8.912737

709

502681

356400829

26.6270539

8.916931

710

504100

357911000

26.6458252

8.921121

711

505521

359425431

26.6645833

8.925308

712

566914

360944128

266833281

8.929400

713

508369

362467097

26 7026598

8.933669

714

509796

363994344

26.7207784

8.937843

715

511225

365525875

26.7394839

8.912014

716

512656

367061696

26.7581703

8.946181

717

514089

368601813

26.7768557

8.950344

718

515524

370146232

26.7955220

8.954503

719

516961

371694959

20 8141754

8.9586658

720

518400

373248000

20 8328157

8.962809

721

519841

374805361

20.8514432

8.966957

722

521284

376367048

208700577

8.971101

723

522729

377933067

20.8886593

8.975241

724

524176

379563424

26.9072481

8.979377

725

5*5625

381078125

26.9258240

8.983509

726

527076

382657176

26.9443872

8.987637

727

528529

384240583

26.9629375

8.991762

728

529984

38582835

26.9814751

8.995883

729

531411

387420189

27.00000o0

9.600006

730

532900

389017000

270185122

9.004113

731

534361

390617891

27 0370117

9.008223

732

535824

392223168

27.0554985

9.012329

733

527289

393832837

27.0739727

9.016131

734

530796

395446904

27.6921341

9.020529

735

540223

397065375

27.1108834

9.021621

736

541696

398688256

27 1293199

9.028715

737

543169

400315553

27.1477439

9.032802

No.

Square.

Cube.

Sq. Root

CubeRook

738

514644

401947*72

271661554

9.036880

739

546121

403583419

27.1845514

9.040965

740

547600

405224600

27.2029410

9.045042

741

549081

406869021

27.2213152

9.049114

742

550564

408518488

27.2396769

9.053183

743

552049

410172407

27.2530263

9.057243

744

553536

411830784

27.2763634

9.061310

745

555025

413493025

27.2946881

9.065365

746

556516

415160936

27.3130006

9.069422

747

558009

4168327*3

27.3313007

9.073473

748

559504

418508992

27.3495887

9.077520

749

561001

420189749

27.3678644

9.081563

750

562500

421875000

27.3861279

9.085603

751

564001

4*3561751

27.4043792

9.089635

752

565504

425259008

27.4226184

9.093672

753

567009

426957777

27.4408455

9.097701

754

568516

428661064

274590694

9.101726

755

570025

430368875

27.47/2633

9.105748

756

571536

432081216

274*54542

9.109767

757

573049

433798093

27.5136330

9.113782

758

574564

43551951*

27.5317998

9.117793

759

576081

437*45479

27.5199546

9.12801

700

577606

438976000

27.5680975

9.125805

701

57*121

440711081

27.5862234

9.129860

702

580644

44*4507*8

276043475

9.133803

703

582169

444194947

27 6224546

9.137797

704

583696

445913744

27.6405499

9.141787

705

585225

447697125

27.6586334

9.145774

766

586756

449455096

27 O7o7050

9.149578

767

588289

451217663

27.6947643

9.153737

768

589824

452984832

27.7128129

9.951714

769

591361

454756609

27.7308492

9.161681

770

592900

456533000

277488739

9.165656

771

594441

458314011

27.7668868

9.169622

772

595984

460099648

27.7848880

9.173585

773

597529

461889917

27.8028775

9.177544

774

599076

463084824

27.8208555

9.184500

775

600625

465481375

27.8383248

9.485453

776

602176

467888576

27 3567766

9.189402

777

603729

469097433

27.8747197

9.193347

778

605284

470910952

27.8926544

9.197596

779

606841

472729139

27.9105715

9.201229

786

608400

471452606

27.9284801

9.205104

781

609961

476379541

27.9463772

9.209096

782

6115.4

47o211768

27.9642629

9.213025

783

613089

480048687

27.9821372

9.216900

781

614656

48l890304

28.0600060

9.220879

785

616225

483736625

28.0178515

9.224751

786

617796

485587650

28.0356945

9.228700

787

619369

487443403

28.0535203

9.232019

788

620944

489303872

28.0713377

9.230528

789

622521

491169069

28.0891438

9.240435

790

624100

49039000

28.1069386

9.244335

791

625681

494913674

28.1247222

9.248234

792

627264

496793388

28.1424946

9.252136

793

628849

498677257

28.1662557

9.250022

79

630136

500566184

28.1780056

9.209911

795

0320*5

502459875

28.1957444

9.260797

796

633610

504353336

28.2134720

9.267680

79.

635209

506261573

28 2311884

9.271559

798

636804

508169592

28.2433938

9.275455

799

638401

510682399

28*665331

9.279300

800

640006

512000000

28 2842712

9.283170

801

641601

513922401

28.3019434

9.287044

802

643201

515849668

23.3190045

9.290007

803

644809

517781627

28.3372540

9.29470

804

646416

519718464

28.3548938

9.298621

No.

square.

Cube.

Sq. Root.

CubeRoot.

805

643025

5216691251

283725219

9.302477

806

649636

523606616

28 3901391

9.306328

807

651249

525557943

28.4077454

9.310175

808

652864

527514112

28 4253408

9.3140191

809

654481

529475129

28.4429253

9.317360

810

656100

531441000

28.4604989

9.321697

811

657721

533411731

28.4780617

9.325532

812

659344

53538732S

23.4956137

9.329363

813

660969

537367797

23.5131549

9.3331922

814

662596

539353144

28.5306852

9.337017

815

664225

541343375

28.5482048

9.340839

816

665856

543338496

23.5657137

9.3i4657i

817

607489

5453335133

28.5832119

9.348473

818

669124

547313432

28.6006993

9.352286

819

670761

549353259

28.6181760

9.356095

820

672400

551368000

28.6356421

9.359902

821

674041

553337661

28.6530976

93637051

822

675684

555412248

28.6705424

9 367505

823

677329

557441767

23.6879706

9.371302

824

678976

559476224

23.7054002

9.375096

825

680625

561515625

28.7228132

9.373887

826

632276

563559976

28.7402157

9.382675

827

633929

565609283

28.7576077

9.336460

823

685581

567663552

28.7749891

9.390242

829

687241

569722789

28.7923601

9.394021

830

688900

571787000

28.8097206

9.307796

831

690561

573856191

28.8270706

9.401569

832

692224

575930368

28.8444102

9.405339

833

693889

578009537

28.8617394

9.409105

834

695556

580093704

28.8790582

9.412869

835|

697225

582182875

28.8963666

9.416630

836;

698896

584277056

28.9136646

9.420337

837

700569

586376253

28.9309523

9.424142

838

702244

588480472

28.9482297

9.427894

839

703921

590589719

28.9651967

9.431642

840

705600

592704000

28.9827535

9.435388

841

707281

594823321

29.0000000

9.439131

842

708964

596947688

29.0172363

9.442370

843

710649

599077107

29.0344623

9.4466071

844

712336

601211584

29.0510781

9.450341

845

714025

603351125

29.0688837

9.454072

846

715716

605495736

29.0860791

9.457800

847

717409

607645423

29.1032644

9.461525

848

719104

609300192

29.1204396

9.465247

849

720801

611960049

29.1376046

9.463966

850

722500

614125000

291547595

9.472682

851

724201

616295051

29.1719043

9.476396

852

725904

618470208

29.1890390

9.480106

853

727609

620650477

29.2061637

9.483814

854

729316

622835364

29.2232784

9.487518

855

731025

625026375

29.2403830

9.491220

856

732736

627222016

29.2574777

9.494919

857

734449

629422793

29.2745623

9.498615

858

736164

631623712

29.2916370

9.5023J8

859

737881

633839779

29.3087018

9.505998

860

739600

636056000

293257566

9.509685

861

741321

638277381

29.3423015

9.513370

862

743044

640503928

29.3598365

9.517051

863

744769

642735647

29.3768616

9.520730

864

746196

644972544

29.3933769

9.524406

865

748225

647214625

29.4103823

9.528079

866

749956

649461896

29.4278779

9.531750

867

751689

651714363

29.4448637

9.535417

868

753424

653972032

29.4618397

9.539082

869

755161

656234909

29.4788059

9.542744

87C

756900

658503000

29.1957624

9.546403

871

758641

660776311

29.5127091

9.550059

No.

Square.

Cube.

Sq. Root

CubeRoot.

872

769384

663054848

29.5296461

9.553712

873

762129

665338617

29.5465734

9.557363

874

763376

667627624

29.5634910

9.561011

875

765625

669921875

29.5803989

9.564656

876

767376

672221376

29.59729722

9.568298

877

769129

674526133

29.6141858

9.571938

878

770884

676836152

29.6310648

9.575574

879

772641

679151439

29.6479342,

9.579208

880

774400

681472000

29.6647939

9.582840

881

776161

683797841

29.6816442

9.586468

832

777924

686128968

29.6984848

9.590094

883

779689

688465387

29.7153159

9.593717

834

781456

690807101

29.7321375

9.597337

8.35

783225

693154125

29.7489496

9.600955

886

784996

695506456

29.7657521

9.604570

837

786769

697864103

29.7825452

9.603182

888

788544

700227072

29.7993289

9.614791

889

790321

702595369

29.8161030

9.615398

890

792100

704969000

29.8328678

9.619002

891

793881

707347971

29.8496231

9.622603

892

795664

709732288

29.8663690

9.626202

893

797449

712121957

29.8831056

9.629797

894

799236

714516984

29.8998328

9.633S91

895

801025

716917375

29.9165506

9.636981

896

802816

719323136

29.8332591

9.640569

897

804609

721734273

29.9499583

9.644154

898

806404

724150792

29.9666481

9.647737

899

808201

726572698

29.9833237

9.651317

900

810000

729000000

30.0000000

9.654894

901

811801

731432701

30.0166620

9.658468

902

813604!

733870808

30.0333148

9.662040

903

815409

736314327

30.0499584

9.665610

904

817216

738763264

30.0665923

9.669176

905

819025

741217625

30.0832179

9.672740

906

820836

742677416

30.0998339

9.676302

907

822649

746142643

30.1164407

9.679860

908

824464

748613312

30.1330383

9.683417

909

826281

751089429

30.1496269

9.636970

910

828100

753571000

30.1662063

9.690521

911

829921

756058031

30.1827765

9.694069

912

831744

758550528

30.1993377

9.697615

913

833569

761048497

30.2158899

9.701158

914

835396

763551944

30.2324329

9.701699

915

837225

766060875

30.2489669

9.708237

916

839056

768575296

30.2654919

9.711772

917

840889

771095213

30.2820079

9.715305

918

812724

773620632

30.2985148

9.718835

919

844561

776151559

30.3150128

9.722363

920

846400

778683000

30.3315018

9.725888

921

848241

781229961

30.3479818

9.729411

922

850084

783777448

30.3644529

9.732931

923

851929

786330467

30 3809151

9.736448

924

853776

788889024

30.3973633

9.739963

925

855625

791453125

30.4138127

9.743476

926

857476

794022776

30.4302481

9.746986

927

859329

796597983

30.4466747

9.750493

928

861184

799178752

30.4630924

9.753998

929

863041

801765089

30.4795013

9.757500

930

864900

804357000

30.4959014

9.761000

931

866761

806954491

30.5122926

9.764497

932

868624

809557568

30.5286750

9.767992

933

870489

812166237

30.5150487

9.771484

934

872356

814780504

30.5614136

9.774974

935

874225

817400375

30.57776..7

9.778462

936

876096

820025856

30 5941171

9 781947

937

877969

822656953

30.6104557

9.785429

938

879844

825293672

30.6267857

9.788909

No.

Square.

Cube.

Sq. Root.

CubeRoot.

939

881721

827936019

30.6431069

9.792386

940

883600

830584000!

30.6594194

9.795361

941

885481

833237621

30.6757233

9.799334

942

837364

835896888;

30.6920185

9.802804

943

889249

838561807

30.7083051

9806271

944

891136

841232384

30.7245830

9.809736

945

893025

843908625:

30.7408523

9813199

946

894916

846590536

30.571130

9.816659

947

896809

849278123

30.7733651

9.820117

948

898704

851971392

30.7896086

9.823572

949

900601

854670349;

30.8058436

9.827025

950

902500

857375000!

30.8220700

9.830476

951

904401

860085351

30 8382879

9833924

952

906304

862801408:

30.8544972

9.837369

953

908209

865523177

30.8706981

9.840813

954

910116

868250664

30.8868904

9844254

855

912025

870983875

30.9030743

9.847692

956

913936

873722816

30.9192497

9.851128

957

915849

876467493

30.9354166

9.854562

958

917764

879217912;

30.9515751

9.857993

959

919681

881974079

30.9677251

9.861422

960

921800

884736000

30.9938668

9.864848

961

923521

887503681.

31.0000000

9.868272

962

925444

890277128

31.0161248

9.871694

963

927369

8930563471

31.0322413

9.875113

964

929296

895341344

31.0483494

9.878530

965

931225

898632125

31.0644491

9.881945

966

933156

901428696

31.0805405

9.885357

967

935089

904231063

31.0966236

9.888767

968

937024

907039232

31.1126984

9.892175

969

938961

909853209

31.1287648

9.895580

No.

! Square.

Cube.

Sq. Root.

CubeRoot

970

940900

912673000

311448230

9.838983

971

942341

915498611

31.1608729

9.902333

972

944784

918330048

311769145

9.905782

973

946729

921167317

31.1929479

9.909178

974

948676

921010424

31.2039731

9.912571

975

950625

926859375

31.2249900

9.915962

976

952576

929714176

31.2409987

9.919351

977

954529

932574833

31.2569992

9.922733

978

956484

935441352

31.2729915

9.926122

979

958441

938313739

31.2889757

9.929504

980

960400

941192000

31.3049517

9.932884

981

962361

944076141

31.3209195

9.936261

982

964324

946966168

31.3368792

9.939636

983

966289

949862087

31.3528308

9943009

984

968256

952763904

31.3687743

9.946380

985

970225

955671625

31.3847097

9.949748

986

972196

958585256

31.4006369

9 953114

987

974169

961504803

31.4165561

9.956477

288

976144

964430272

31.4324673

9.959839

989

978121

967361669

31.4483704

9.963198

990

980100

970299000

31.4642654

9.966555

991

982081

973242271

31.4801525

9.969909

992

984064

976191488

31.4960315

9.973262

993

986049

979146657

31.5119025

9.976612

994

988036

982107784

31.5277655

9.979960

995

990025

985074875

31.5436206

9.983305

996

992016

988047936

31.5594677

9.986649

997

994009

991026973

31.5753068

9.989990

998

996004

994011992

31.5911330

9.993329

999

998001

997002999

31.6069613

9.996666

1000

1000000

1000000000

31.6227766

10.000000

The following rules are for finding the squares, cubes, and roots of numbers exceeding 1000.

To find the square of any number divisible without a remainder. Rule. - Divide the given number by such a number from the foregoing table as will divide it without a remainder; then the square of the quotient, multiplied by the square of the number found in the table, will give the answer.

Example. - What is the square of 2000? 2000, divided by 1000. a number found in the table, gives a quotient of 2, the square of which is 4, and the square of 1000 is 1,000,000, therefore:

4 x 1,000,000 = 4,000,000: the Ans.

Another Example. - What is the square of 1230? 1230, being divided by

123, the quotient will be 10, the square of which is 100, and the square of 123 is 15,129, therefore:

100 x 15,129 = 1,512,900: the Ans.

To find the square of any number not divisible without a remainder. Rule. - Add together the squares of such two adjoining numbers from the table as shall together equal the given number, and multiply the sum by 2; then this product, less 1, will be the answer.

Example. - What is the square of 1487? The adjoining numbers, 743 and 744, added together, equal the given number, 1487, and the square of 743 = 552,049, the square of 744 = 553,536, and these added = 1,105,585, therefore:

1,105,585 x 2 = 2,211,170 - 1 = 2,211,169: the Ans.

To find the cube of any number divisible without a remainder. Rule. - Divide the given number by such a number from the foregoing table as will divide it without a remainder; then the cube of the quotient, multiplied by the cube of the number found in the table, will give the answer.

Example. - What is the cube of 2700? 2700, being divided by 900, the quotient is 3, the cube of which is 27 and the cube of 900 is 729,000,000, therefore:

27 x 729,000,000 = 19,683,000,000: the Ans.

To find the square or cube root of numbers higher than is found in the table. Rule. - Select, in the column of squares or cubes, as the case may require, that number which is nearest the given number; then the answer, when decimals are not of importance, will be found directly opposite, in the column of numbers.

Example. - What is the square root of 87,620? In the column of squares, 87,616 is nearest to the given number; therefore, 296, immediately opposite in the column of numbers, is the answer, nearly.

Another example. - What is the cube root of 110,591? In the column of cubes, 110,592 is found to be nearest to the given number; therefore, 48, the number opposite, is the answer, nearly.

To find the cube root more accurately. Rule. - Select from the column of cubes that number which is nearest the given number, and add twice the number so selected to the given number; also, add twice the given number to the number selected from the table. Then, as the former product is to the latter, so is the root of the number selected to the root of the number given.

Example. - What is the cube root of 9200? The nearest number in the column of cubes is 9261, the root of which is 21, therefore:

9261 9200

2 2

18522 18400

9200 9261

As 27,722 is to 27,661, so is 21 to 20.953 + , the Ans.

Thus, 27,661 x 21 = 580,881, and this divided by 27,722 = 20.953 +.

To find the square or cube root of a whole number with decimals. Rule. - Subtract the root of the whole number from the root of the next higher number, and multiply the remainder by the given decimal; then the product, added to the root of the given whole number, will give the answer correctly to three places of decimals in the square root, and to seven in the cube root.

Example. - What is the square root of 11.14? The square root of 11 is 3.3166, and the square root of the next higher number, 12, is 3.4641; the former from the latter, the remainder is 0.1475, and this by 0.14 equals 002065. This added to 3.3166, the sum, 3.33725, is the square root of 11.14.

To find the roots of decimals by the use of the table. Rule. - Seek for the given decimal in the column of numbers, and opposite in the columns of roots will be found the answer, correct as to the figures, but requiring the decimal point to be shifted. The transposition of the decimal point is to be performed thus: For every place the decimal point is removed in the root, remove it in the number two places for the square root and three places for the cube root.

Examples. - By the table, the square root of 86.0 is 9.2736, consequently by the rule the square root of 086 is 0.92736. The square root of 9. is 3., hence the square root of 009 is 0.3. For the square root of 0.0657 we have 0.25632, found opposite No. 657. So, also, the square root of 0.000927 is 0.030446, found opposite No. 927. And the square root of 8.73 (whole number with decimals) is 2.9546, found opposite No 873. The cube root of 0.8 is 0.928, found at No. 800; the cube root of 0.08 is 0.4308, found opposite No. 80, and the cube root of 0.008 is 0.2, as 2.0 is the cube root of 8.0. So also the cube root of 0.047 is 0.36088, found opposite No. 47.