I am having a little troubles with this problem, I think there is something subtle that I am missing

a) Show that $\displaystyle \sqrt[4]{2} \not\in \mathbb{Q}(\sqrt{2})$ where $\displaystyle \mathbb{Q}(\sqrt{2})$ = $\displaystyle \{a+\sqrt{2}b \colon a,b\in\mathbb{Q}\}$

b) Find a minimal polynomial $\displaystyle m_{\sqrt[4]{2}}(x)$ in $\displaystyle \mathbb{Q}(\sqrt{2})[x]$ where $\displaystyle m_{\sqrt[4]{2}}(\sqrt[4]{2}) = 0$

c) Show if $\displaystyle \alpha$ is a primitive element in $\displaystyle GF(p^{n})$, the degree of the minimal polynomial of $\displaystyle \alpha$ is n