Question

Write the rationalising factor for $x\sqrt{mn}$

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 $\sqrt{mn}$ to $x\sqrt{mn}$ to make $\sqrt{mn}$ a rational number as shown below:

$\left(\sqrt{mn}\right)\times \left(x\sqrt{mn}\right)=x\left(mn\right)=xmn$

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