Prove that the following is irrational
`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