Question

Prove that the following is irrational

`1/sqrt2`

Answer 1

`1/sqrt2`

`1/sqrt2 xx sqrt2/sqrt2 = sqrt2/2`

Let a = `(1/2)sqrt2` be a rational number

⇒ 2a = `sqrt2`

2a is a rational number since product of two rational number is a rational number.

Which will imply that `sqrt2` is a rational number. But it is a contradiciton since `sqrt2` is an irrational number.

Therefore 2a is irrational or a is irrational

Therefore `1/sqrt2` is irrational. Hence proved