Question

Write the simplest rationalising factor of `sqrt(72)`.

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(72)`

Prime factors of 72 is 2 × 2 × 2 × 3 × 3

So, `sqrt(72) = sqrt(2 xx 2 xx 2 xx 3 xx 3)`

= `2 xx 3 xx sqrt(2)`

= `6sqrt(2)`

If we multiply `6sqrt(2)` by `sqrt(2)`, we get

`6sqrt(2) xx sqrt(2)`

= 6 × 2

= 12

→ rational number

Hence, `sqrt(2)` is the rationalising factor of `6sqrt(2)`.