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

Answer:

The square root of a number and squaring a number are inverse operations. If we represent the square root of x as x to the power of 'n', then $(\sqrt{x})^2 = (x^n)^2 = x^1$. According to the power of a power rule, $(x^n)^2 = x^{2n}$. Therefore, $2n = 1$, which means $n$ must be $1/2$. Thus, the square root of a number is equal to that number raised to the $1/2$ power.