# Prove that if m, n are natural, then the root

by rangerjoe
Tags: natural, prove, root
 P: 1 Hi, I've encountered this exercise which I'm having a hard time proving. It goes like this: Prove that if m and n are natural, then the nth root of m is either integer or irrational. Any help would be greatly appreciated. Thanks.
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,895 I would imagine you would start by proving it for m= p, a prime number. That would make it easy to prove "If integer k is not divisible by p then neither is kn" so you could mimic Euclid's proof that $\sqrt{2}$ is irrational. After that, look at products of prime.
 P: 107 if p is prime and divides m^n, p must divide m...

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