1. The problem statement, all variables and given/known data Prove these propositions 2. Relevant equations If x is rational, then x + sqrt(2) is irrational. If x + sqrt(2) is irrational, then x is rational. If xsqrt(2) is irrational, then x is rational. 3. The attempt at a solution I've tried a couple of ways, but I always end up at a dead end. usually, I end up assuming what I need to prove.