I have to show that, for any prime $p$ and $n \in \mathbb{N}_{\geq2}$, $X^n-p$ is irrededucible over $\mathbb{Q}$. (We haven‘t looked at stuff like the Eisenstein‘s criterion yet in class.)
I was able to show that for any $m<n$: $p^{m/n}\notin \mathbb{Q}$, but now I don‘t know what to do, I suppose I could write out a general polynomial division but there surely must be a better way.
Any help is appreciated:)