Question

Write the rationalising factor for $8\sqrt{x-y}$

Answer 1

We know that If the product of two surds is a rational number, then each factor is a rationalising factor of the other.

Now multiply $\sqrt{x-y}$ to $8\sqrt{x-y}$ to make $\sqrt{x-y}$ a rational number as shown below:

$\left(\sqrt{x-y}\right)\times \left(8\sqrt{x-y}\right)=8(x-y)$

Hence, $\sqrt{x-y}$ is the rationalising factor of $8\sqrt{x-y}$.