Determine the degree of the extension over Q Determine the degree of the extension $Q(\sqrt{3+2 \sqrt{2}})$ over Q.
I can see that $$3+2 \sqrt{2} = (1+ \sqrt2)(1+ \sqrt2) =(1+ \sqrt2)^2$$ does that mean $$x^2 -(1+ \sqrt2)^2)$$ has a degree $2$. Is this correct

Example: Let $p(x) = \sqrt{1+\sqrt{2}}$.
Let $u = \sqrt{1+\sqrt{2}} \Rightarrow u^2 = (1+\sqrt{2})^2 = 2+2\sqrt{2} \Rightarrow (u^2-2)^2 = 8 \Rightarrow u^4-4u^2+4=8 \Rightarrow u^4-4u2-4=0$
Hence $u$ is the root of $x^4-4u^2-4$. Try this techniques with your adjoined root and see if you can say anything about the polynomial that it satisifies over $\mathbb{Q}$.
