Question of the Day

For what values of rational $p$ and $q$ will $p\sqrt{2}+q\sqrt[3]{3}$ be rational? You may assume $\sqrt[3]{3}$ is irrational and of course $\sqrt{2}$ is irrational too. Recall though that the sum of two irrationals can be either rational or irrational. Hint: remember how to compare surds.