Irreducibility of $x^p-a \in \Bbb Q[x]$, where $a(>0) \in \Bbb Q $ with $ a^{1/p} \notin \Bbb Q$

Question

Let $p$ be a prime, and $a$ be a positive rational number such that $a^{1/p}$ is irrational. Then is the polynomial $x^p-a$ always irreducible in $\Bbb Q[x]$? Intuitively it seems obvious, but I don't see how to prove it.