Question

Write the rationalising factor for $5p\sqrt{a+b}$

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 $\sqrt{a+b}$ to $5p\sqrt{a+b}$ to make $\sqrt{a+b}$ a rational number as shown below:

$\left(\sqrt{a+b}\right)\times \left(5p\sqrt{a+b}\right)=5p(a+b)$

Hence, $\sqrt{a+b}$ is the rationalising factor of $5p\sqrt{a+b}$.