Question

Write the rationalising factor for $\sqrt{xy}$

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 $\sqrt{xy}$ to itself to make $\sqrt{xy}$ a rational number as shown below:

$\Rightarrow \left(\sqrt{xy}\right)\times \left(\sqrt{xy}\right)=xy$

Hence, $\sqrt{xy}$ is the rationalising factor of $\sqrt{xy}$.