Question

Write the simplest rationalising factor of `sqrt(7) - sqrt(5)`.

Answer 1

When a surd is multiplied by another surd to obtain a rational number, it is called rationalisation. Each surd is called the rationalising factor of the other.

Given, `sqrt(7) - sqrt(5)`

If we multiply `sqrt(7) - sqrt(5)` with `sqrt(7) + sqrt(5)` we will get 

`(sqrt(7) - sqrt(5))(sqrt(7) + sqrt(5))`

= `(sqrt(7))^2 - (sqrt(5))^2`

= 7 – 5

= 2

→ rational number

Hence, `sqrt(7) + sqrt(5)` is the rationalising factor of `sqrt(7) - sqrt(5)`.