Prove that the following is irrational
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.