Compute the degrees of and over .
Let . Evidently, . (WolframAlpha agrees.) That is, is a root of . Thus the minimal polynomial of over has degree 1, and the extension has degree 1 over .
Similarly, let . Evidently, (WolframAlpha agrees), so that is a root of . is irreducible by Eisenstein’s criterion, and so is the minimal polynomial of over . The degree of over is thus 2.