Question

Explain why the square root of a number is defined to be equal to that number to the 1/2 power

Answer 1

because all you do is times that number by itself then when you divide you have to take half of the number then divide it

Answer 2

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.