Prove that $\sqrt[5]{672}$ is irrational How would you prove $\sqrt[5]{672}$ is irrational? 
I was trying proof by contradiction starting by saying:

Suppose $\sqrt[5]{672}$ is rational ...


$$672^{1/5}=\frac pq,$$($p$ and $q$ relative primes) then
$$p^5=672q^5,$$
which is possible only if $p$ is a multiple of $7$, which in turn implies that $q$ is a multiple of $7$.
