I would like to know if $\mathbb Q \left[\sqrt {2+\sqrt 2}\right ]: \mathbb Q$ is normal . The roots of the minimal polynomail is $\pm\sqrt {2\pm\sqrt 2}$ .
Now the thing that i have really tried and have no idea to get is to write $\sqrt {2-\sqrt 2}$ as the combination of the powers of $\sqrt {2+\sqrt 2}$
If at all it is possible ??
What are the possible ways of finding the coefficients ?
Thanks for you help .