Question: proof that root 2 plus root 3 is irrational?
Answer: If √2+√3 is rational, then so is (√2+√3)2=5+2√6. But this is absurd since √6 is irrational. If √3+√2 is rational/irrational, then so is √3−√2 because √3+√2=1√3−√2 .