Prove that for any distinct primes $p$ and $q$, the ratio $\frac{\sqrt p}{\sqrt q}$ is irrational.
I know that separately $\sqrt p$ and $\sqrt q$ are irrational, so my initial thought process was to show that they are each irrational, but it is not always true that an irrational number divided by an irrational number is also irrational, could someone lead me in the right direction?
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