Question

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

Answer 1

This is essentially a rule in the unit of radicals, where n✔️X^m = X^m/n. If the value of m is equal to n, as in 2✔️3^2 it would simply be 3^2/2 which is nothing but 3^1 = 3. Basically, the m value can be greater than n and or less than n, but if it is equal the m and n values cancel out.

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.