Question

Write the simplest rationalising factor of `sqrt(6) + sqrt(3)`.

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(6) + sqrt(3)`

If we multiply `sqrt(6) + sqrt(3)` with `sqrt(6) - sqrt(3)` we will get

`(sqrt(6) + sqrt(3))(sqrt(6) - sqrt(3))`

= `(sqrt(6))^2 - (sqrt(3))^2`

= 6 – 3

= 3

→ rational number

Hence, `sqrt(6) - sqrt(3)` is the rationalising factor of `sqrt(6) + sqrt(3)`.