Question

Prove that 7-4√2 is irrational

Answer 1

Consider, 4−3√2 Let 4−3√2 = (a/b) a rational number  ⇒ −3√2 = (a/b) − 4⇒ −3√2 = (a − 4b)/b ⇒ √2 = (a − 4b)/(−3b) Since a, b are integers, then (a − 4b)/(−3b) represents a rational number. But this is a contradiction since RHS is a rational number where as LHS (√2) is an irrational number Hence our assumption that " 4−3√2 = (a/b) is a rational number" is incorrect.Thus  4−3√2 is an irrational number