First the easy one (I think): Show that x4-22x3+1 is irreducable (is that how it's spelled?) over Q. Now the one that's giving me a headache: Suppose E/F, when [E:F]=2, and char(E)>2. Prove that there exists u in E, s.t. E=F(u), when u is a root of p(x)=x^2-a, for a in F. Tried all kinds of stuff, it just won't lead me anywhere. I guess it's probably easy, but it's bothering me. Thanks in advance!