The question is to determine the dimension over Q(rationals)of the extension Q(sqrt(3+2sqrt2)). So we need to find [Q(sqrt(3+2sqrt2)): Q]. All I can say is that (3+2sqrt2) = (1+sqrt2)^2. I also know that we're trying to find the degree of the minimum polynomial over Q that has sqrt(3+2sqrt2) as a root. But I don't know how to proceed.