Question: given that root 2 is irrational proof that 5 + 3 root 2 is an irrational number?
Answer: As 5 + 3√2 is rational. (Assumed) They must be in the form of p/q where q≠0, and p & q are co prime. ... And, Rational ≠ Irrational. Therefore we contradict the statement that, 5+3√2 is rational.