This section is from the book "The American House Carpenter", by R. G. Hatfield. Also available from Amazon: The American House Carpenter.

We have seen that the square of a is a1 x a1 = a2; of 2 a3 is 2 a3 x 2 a3 = 4 a6; in each case the square is obtained by doubling the exponent.

To obtain the square root the converse follows, namely, take half of the exponent.

Thus the square root of a1 is a2, of a3 is a, of a6 is a3.

The same rule, when the exponent is an odd number, gives a fractional exponent, thus: the square root of a3 is a3/2; or, of a5, is a5/2 So. also, the square root of a, or a1 is a1/2.

Therefore, we have equals the square root of a, and the cube root of

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