This has to be proven or disproven using a counter example:
Let $p,q\in\mathbb{R}$ \ $\mathbb{Q}$, then $\frac { p }{ q }$ is irrational.
$p,q\in\mathbb{R}$ \ $\mathbb{Q}$ $\Rightarrow p,q\in\mathbb{R}$ such that $p,q\notin\mathbb{Q}$
Thus $p,q$ are irrational.
If $p=q=\sqrt { 2 } $, then $p,q$ are irrational, but $\frac { p }{ q } =\frac { \sqrt { 2 } }{ \sqrt { 2 } } =1$, which is rational.