Let $\displaystyle \mathbb{Q}[\sqrt{n}] = \{a + b\sqrt{n}\}$

Prove that both $\displaystyle \mathbb{Q}[\sqrt{2}]$ and $\displaystyle \mathbb{Q}[\sqrt{5}]$ are fields but that they are not isomorphic.

Note: rings are commutative and associative with unity.

To prove they are fields, just find the general multiplicative inverse.

How do I prove they are not isomorphic?