Irrational and rational proofs

Hey, I was wondering about proving that square roots of numbers are rational or irrational.
I know about proving this for the numbers 1(duh), 2 and all multiples of 2 and 4, but what about 3?
How do i prove that 3(or any other number) is irrational or rational?

This is an answer set forward by Gabriel Haeseron orkut

let k and n be positive integers, if k^(1/n) is not an integer than it is irrational.

proof: supose k^(1/n)=a/b, than k.b^n=a^n. we know k is not the n-th power of an integer, so there must be a prime factor p of k with multiplicity alpha, such that alpha is not a multiple of n. So, p must appear with multiplicity beta in kb^n, such that beta is not a multiple of n, but that is a contradiction because the multiplicity of p in a^n is clearly a multiple of n. That concludes the proof.