Determining if (3) is a maximal ideal in $\mathbb{Z}[\sqrt{7}]$.

Question

As far as I can tell, the tools I have for determining if an ideal I of a ring R is maximal is either: Determine another ideal it is contained within, or look at the quotient ring $R/I$ and determine if it is a field.

I have attempted the first without any success, as my only result was the ideal $(\sqrt{7})$, which, as near as I can tell, is equal to R. The second method, I have no idea where to even start.

Answer 1

Note:

$$(\sqrt{7}-1)(\sqrt{7}+1)\in\langle3\rangle$$