Question

prove that 4-3/2 is an irratioal number​

Answer 1

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