Question

Why does `sqrtx=x^(1/2)`?

Answer 1

The reason this is true is that fractional exponents are defined that way.

For example, `x^(1/2)` means the square root of `x`, and `x^(1/3)` means the cube root of `x`. In general, `x^(1/n)` means the `n`th root of `x`, written `root(n)(x)`.

You can prove it by using the law of exponents:

`x^(1/2)*x^(1/2)=x^((1/2+1/2))=x^1=x`

and

`sqrtx*sqrtx=x`

Therefore, `x^(1/2)=sqrtx`.