Question

Prove that 4-5 root 2 is an irrational no.

Answer 1

let (4-5√2) be a rational number.
so,
(4-5√2) = p/q.
√2 = 4q-p/5q ,which is a rational number
but √2 is an irrational number
so, 4-5√2 is an irrational number...

Answer 2

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.