I'm taking my first proof heavy class, linear algebra. Unfortunately, I'm taking a long time picking up proofs in general, so I'm going to try and work through some of the material in Hoffman/Kunze. 1. The problem statement, all variables and given/known data Prove that the set of all complex numbers in the form of x + y√2, where x and y are rational, is a subfield of C. 2. Relevant equations The nine rules of algebra... x+y=y+x . . . 3. The attempt at a solution In general, a subfield has to obey the nine rules of algebra (addition and multiplication) and if x and y are elements of the field F, then so are (x+y), -x, xy, and x^-1. I'm not going to spend time writing a proof in this particular post. I just want some general guidance on how to approach certain proofs. For this one, my first idea is to define two numbers, (x1+y1√2) and (x2+y2√2), and then show that "(x+y), -x, xy, and x^-1" are all complex numbers. I'll do this by simple addition/multiplication and, which stem from the nine rules. Would this work? Sorry for the lack of LaTeX. I just want to get this question out before dinner.