Question: prove that √ 2 + √ 3 is irrational?
Answer: If √2+√3=r∈Q, then r2−52=√6∈Q. ... Then its square is rational, because multiplying rationals gives a rational. But (√2+√3)2=2+2√6+3 is irrational because the sum of an irrational and a rational (5) is irrational, so we have a contradiction.