Question: prove that root 3 plus root 2 is irrational?
Answer: If √3+√2 is rational/irrational, then so is √3−√2 because √3+√2=1√3−√2 . Now assume √3+√2 is rational. ... But the sum of two rationals can never be irrational, because for integers a,b,c,d ab+cd=ad+bcbd which is rational.