The cube root of a number is found in the same manner as the square root, except the given number is pointed off into periods of three figures each. The following numbers would be pointed off thus: 3141.6, 3'141.6; 67296428, 67'296'428; 601426.314, 601'426.314; .0000000217, .000'000'021'700.

Having pointed off, move the decimal point so that it will fall between the first and second periods of the significant part of the number, as in square root. In the above numbers the decimal point will be placed thus: 3.1416, 67.296428. 601.426314, and 21.7.

If the given number has but three (or less) significant figures, find the significant part of the number in the column headed n; the cube root will be found in the column headed according to whether one, two. or three figures precede the decimal point after it has been moved. Thus, the cube root of 21.7 will be found opposite 2.17, in column headed while the cube root of 2.17 would be found in the column headed and the cube root of 217 in the column headed all on the same line. If the given number contains more than three sig nificant figures, proceed exactly as described for square root except that the column headed n3 is used.

(a) =? (6) =?

### Solution

(a) Pointing off into periods, we get 000'006'241'700; moving the decimal point, we get 6.2417. The number falls between 6.22950 = 1.843 and 6.33163 = 1.853; the first difference = 10213; the second difference

6.24170 - 6.22950 = 1220; 1220/10213= .119+, or .12, the fourth and fifth figures of the root. The decimal point is located by the rule previously given; hence, = .018412.

(6) =? As the number contains more than six significant figures, reduce it to six significant figures by replacing all after the sixth figure with ciphers, increasing the sixth figure by 1 when the seventh is 5 or a greater digit. In other words, the first five figures of and of are the same. Pointing off into periods, we get

50'932'700; moving the decimal point, we get 50.9327, which falls between 50.6530 = 3.703 and 51.0648 = 3.713; the first difference is 4118; the second difference is 2797; 2797/ 4118 = .679+, or .68. The integral part of the root evidently contains three figures; hence, = 370.68, correct to five figures.