• ## Prove that there is no rational number whose square is 2

Let $p/q$ be a rational number whose square is $2$, where we assume that $p/q$ is in lowest terms, i.e. $p$ and $q$ have no common integer factors except $\pm1$ (integers relatively prime).

Then $(p/q)^2=2$, $p^2=2q^2$ and $p^2$ …