Question

Write the rationalising factor for $4\sqrt{p+q}$

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 $\sqrt{p+q}$ to $4\sqrt{p+q}$ to make $\sqrt{p+q}$ a rational number as shown below:

$\left(\sqrt{p+q}\right)\times \left(4\sqrt{p+q}\right)=4(p+q)$

Hence, $\sqrt{p+q}$ is the rationalising factor of $4\sqrt{p+q}$.