proof verification - How to prove that $n sqrt{17}$ is irrational?

Prove that $\sqrt{17}$ is irrational. Subsequently, prove that $n \sqrt{17}$ is irrational too, for any natural number $n \neq 0$. Use the following lemma: Let p be a prime number; if $p | a^2$ then $p | a$ as well. I proved by contradiction that $\sqrt{17}$ is irrational, but I'm not sure how to prove that $n \sqrt{17}$ is irrational. I tried to prove it by contradiction as well, but I'm not sure if that's what I'm supposed to do. Is it easier to prove with induction?