1. The problem statement, all variables and given/known data Let p be a prime and let n≥2 be an integer. Prove that p1/n is irrational. 2. Relevant equations We know that for integers a>1 and b such that gcd(a,b)=1, a does not divide b^n for any n≥ 1. 3. The attempt at a solution To prove irrationality, assume p^(1/n)=a/b for integers a and b≠0. This is equivalent to an=pbn If we've assumed a and b have been reduced to lowest terms, gcd(a,b)=1. Then the proof by contradiction would follow directly if it were just a=pbn But what do I do since it's an?