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

by rangerjoe
Tags: natural, prove, root
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rangerjoe
#1
Nov4-07, 05:38 AM
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.
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HallsofIvy
#2
Nov4-07, 07:07 AM
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Thanks
PF Gold
P: 39,361
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 [itex]\sqrt{2}[/itex] is irrational.

After that, look at products of prime.
matticus
#3
Nov4-07, 05:15 PM
P: 107
if p is prime and divides m^n, p must divide m...


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