# How to define $\mathbb{Q}_p(\sqrt{5})$ and $\mathbb{Q}_p (\sqrt{5} \sqrt{3})$ and find their valuation rings for $p=7$?

I tried finite extension $\mathbb({Q}_p$ I unable do it. It will also great if help me with how to define the valuation ring of that finite extension

Did you mean $\mathbb{Q}_p (\sqrt{5}, \sqrt{3})$ instead of $\mathbb{Q}_p (\sqrt{5} \sqrt{3})$?