# How can you prove that the square root of two is irrational?

I have read a few proofs that $\sqrt{2}$ is irrational.

I have never, however, been able to really grasp what they were talking about.

Is there a simplified proof that $\sqrt{2}$ is irrational?

You use a proof by contradiction. Basically, you suppose that $$√2\sqrt{2}$$ can be written as $$p/qp/q$$. Then you know that $$2q2=p22q^2 = p^2$$. As squares of integers, both $$q2q^2$$ and $$p2p^2$$ have an even number of factors of two. $$2q22q^2$$ has an odd number of factors of 2, which means it can’t be equal to $$p2p^2$$.