Question

Prove that the following is irrational

` 7sqrt5`

Answer 1

Let a = `7sqrt5` be a rational number.

⇒ `a/7 = sqrt5.`

Now, `a/7` is a rational number since product of two rational number is a rational number.

The above will imply that `sqrt5` is a rational number. But `sqrt5 ` is an irrational number.

This contradicts our assumption. Therefore we can conclude that `7sqrt5` is an irrational number and hence the result.