Question

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

Answer 1

see below

Explanation:

There are different ways of proving this, but I like this one...

The `sqrt(x)` is defined to be the opposite of `x^2` meaning that
`sqrt(x^2)=x`

Lets say we don't no the power of the square root jet

`sqrt(x)=x^n`

We do know that `(x^a)^b=x^(a*b)`

Therefore, we can say that

`sqrt(x^2)=x`

`(x^2)^n=x`

`x^(2*n)=x^1`

Now, we can say that `2n=1`

which leads us to `n=1/2`