Question

Prove that 4 - 5 root 2 is a rational number

Answer 1

Consider, 4−5√2

Let 4−5√2 = (a/b) a rational number

⇒ −5√2 = (a/b) − 4

⇒ −5√2 = (a − 4b)/b

⇒ √2 = (a − 4b)/(−5b)

Since a, b are integers, then (a − 4b)/(−5b) represents a rational number.