1.Find the degree and basis for Q(3^1/2,7^1/2) over Q.
2.For any positive integers a, b, show that Q(a^1/2+b^1/2)=Q(a^1/2,b^1/2)
1. Well I know if I looked at (3)^1/2 over Q
Then (3)^1/2 has minimal polynomial x^2-3, so degree 2 over Q
(7)^1/2 has minimal polynomial x^2-7 so degree 2 over Q
so entire thing has degree 2.
Really unsure about basis
2.I started by computing the minimal polynomial of a^1/2+b^1/2 over Q
I don't know how that would hekp me, though