(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

if n>1, prove that [tex]\sqrt[n]{n}[/tex] irrational

2. Relevant equations

n/a

3. The attempt at a solution

so suppose it is rational, so i know [tex]\sqrt[n]{n}[/tex] must be integer, say p

then [tex]n=p^n[/tex] and how do i prove this is not true??

i can prove if p>1 then [tex]p^n>n[/tex] for all n>1 by induction, and when p=1 its clearly contradiction, so i don't know the case when p<1

or rather someone have other easy way to prove the question? clue please T_T

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# Homework Help: Proving that n-th root of n is irrational

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