Question

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

Answer 1

Explanation:

This is due to radical to exponent change property which is

`\sqrt[n]{x}=x^{(1)/(n)}`

We can consider some examples as below;

`\sqrt[3]{4}=4^{(1)/(3)}`

`\sqrt[2]{5}=5^{(1)/(2)}`

Hence, the square root of a number is defined to be equal to that number to the
`(1)/(2)` power.

Or we sometimes solve square root by taking the power as
`(1)/(2)`

Answer 2

Well, the reason for this is that it is actually a well known rule:

X ^m/n = n th root of ✔️x^m.

4^1/2 = ✔️4 = 2.

You are simply raising the base to the first number in the fraction and then taking the appropriate root, for example cube root, fourth root, etc depending on the value of the second number in the fraction.