Question

Write the simplest rationalising factor of `5sqrt(3) + 8`.

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, `5sqrt(3) + 8`

If we multiply `5sqrt(3) - 8` with `5sqrt(3) + 8` we will get

`(5sqrt(3) + 8)(5sqrt(3) - 8)`

= `(5sqrt(3))^2 - (8)^2`

= 75 – 64

= 11

→ rational number

Hence, `5sqrt(3) - 8` is the rationalising factor of `5sqrt(3) + 8`.