How to prove irreducibility of this polynomial? Let $p,q$ be primes.  Prove that $y^{n }-p$ is irreducible over $\mathbb{Q}(\sqrt[n ]q) $ . 

I have tried for some time, but still feel confused about how to prove it. Can anyone help me?
Any root of a prime will be irrational. You can imagine trying to find roots of the polynomial in R and find there are no solutions in terms of radicals of other primes.
Any root of a prime will be irrational. You can imagine trying to find roots of the polynomial in R and find there are no solutions in terms of radicals of other primes.