I have read a few proofs that √2 is irrational.
I have never, however, been able to really grasp what they were talking about.
Is there a simplified proof that √2 is irrational?
You use a proof by contradiction. Basically, you suppose that √2 can be written as p/q. Then you know that 2q2=p2. As squares of integers, both q2 and p2 have an even number of factors of two. 2q2 has an odd number of factors of 2, which means it can’t be equal to p2.