Hi. I'm not sure if I put it in the correct section. I hope I did.

I was wondering if there is a relatively short proof of the following:

$\displaystyle x \in R, x \ge 0, n \in N \setminus \left\{ 0\right\} \Rightarrow \exists ! y \in R: y \ge 0 \wedge y^n=x$

Which means that each number x has only one nth root. There is a proof in Walter Rudin's book but it is really long, so this is why I'm asking , if you know any simpler ones.