I have two questions:

Determine the degree of the extension degree of $ \mathbb{Q}(\sqrt{2 + \sqrt{7}})$ over $ \Bbb Q$ and the degree of the splitting field of the minimal polynomial of $ \sqrt{2 + \sqrt{7}}$ over $ \Bbb Q$ .

For the first one, that’s what I have thought:

$ $ x =\sqrt{2 + \sqrt{7}} \implies x^2 = 2 + \sqrt7 \implies x^4 – 4x^2 -3 = 0$ $

Now $ m_{a}(x) = x^4 – 4x^2 – 3$ is irreducible in $ \mathbb{Q}$ and it is the minimal polynomial of $ \sqrt{2 + \sqrt{7}}$ , so the degree of $ \mathbb{Q}(x)$ should be $ 4$ . Am I correct?

About the second question: how can I find the degree of the splitting field of $ m_{a}(x)$ ? The only thing I know is that $ m_{a}(x)$ has $ 4$ roots, which are $ \pm\sqrt{2 \pm \sqrt{7}}$ . What now?