# Math

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Why is raising a number to the power of 1/2 the same as finding the square root of the number?

• Math -

Patience, child. I've deleted 3 of these duplicate posts in the last few minutes. Do not post this question again for at least 3 hours.

• Math -

Sorry, I didn't know that you delete duplicate posts. I have only just started using this site a couple days ago.

• Math -

We know that
(√x)^2 = x , by the very definition of √x

suppose we take x(1/2) and square it
(x^(1/2)^2
by the exponents rules this would be
x( (1/2)(2) )
= x
so (√x)^2 = (x^(1/2) )^2
then √x = x^(1/2)

so x^(1/2) behaves the same way as √x

by the same argument we can show that
x^(1/3) is the same as ∛x
x^(1/4) is the same as ∜x
etc

• Math -

Thank you. I appreciate it.

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