# Degree of $\mathbb{Q}(\sqrt{2 + \sqrt{7}})$ and splitting field

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?