Let $n$ be a square free integer and alpha belong to $\mathbb{Z}[\sqrt{n}]$. If $N(\alpha)$ is a prime integer, then $\alpha$ is irreducible in $\mathbb{Z}[\sqrt{n}]$.
Here $N(\alpha)$ denotes the norm of $\alpha$.
How can I show this? I'll get back in the morning because it's super late right now!