Let $\alpha = \sqrt{2+\sqrt{2}}$
a) find the minimal polynomial of $\sqrt{2}$ over the rationals
b) find the minimal polynomial of $\alpha$ over $\mathbb{Q}(\sqrt{2})$
c) determine $[\mathbb{Q}(\alpha):\mathbb{Q}]$
d) Find the minimal polynomial of $\alpha$ over rationals.
This is not a homework assignment. This is additional material not covered in my course since it is not for galois theory, only because we didn't get enough time to cover it, but I will be taking the next math class for this, and would appreciate help on this and explanations.