Field Show that F is a field under + and $\cdot$ and F = $\{a + b\sqrt{3}\} | a, b \in \mathbb Q\}$
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field