Can someone help me with the following question please ...

(i) Let $\displaystyle \alpha=\sqrt(\sqrt5+\sqrt15) $. Find the minimum polynomial of $\displaystyle \alpha$ over Q.

(ii) Give a basis for Q($\displaystyle \alpha$) over Q.

(iii) What is [Q($\displaystyle \alpha$):Q] ?

So far for the minimum polynomial I got $\displaystyle (\alpha^8)-40(\alpha^4)+100=0$. Is this correct?

How do I find the required basis?

Thanks.