Let a = (1+(3)^1/2)^1/2. Find the minimal polynomial of a over Q.
The Attempt at a Solution
Maybe the first thing to realize is that Q(a):Q is probably going to be 4, in order to get rid of both of the square roots in the expression. I also suspect that +/-(3)^1/2 will be roots of the minimal polynomial, as Q(a):Q = [Q(a):Q((3)^1/2)]*[Q(3^1/2):Q]. I do not know where to go from here, any advice PF?