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?

I don't know why, but probability still doesn't strike me right. I have a bit of OCD and it seems like messy guesswork, although I know it has some good results.

>>24
I agree, that there's something in probability that disagrees with me on an abstract.

>>17
>>19
Exactly the kind of confusions I came across when first encountering continuous probability distributions. For a distribution positive on [0,1], the probability of being picked, for each number in the set, is zero, but the probability of an individual number being picked is 1. LOL.