Question

Explain why the square root of a number is defined to be

equal to that number to the 1/2 power.

Answer 1

The square root is the inverse operation to the power of 2, so that whenever you take a number and perform both actions on it, you get the same number back.

Answer 2

Sample Answer: Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.