Question

Write the rationalising factor $\frac{1}{2}\sqrt{p}$

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 $\sqrt{p}$ to $\frac{1}{2}\sqrt{p}$ to make $\sqrt{p}$ a rational number as shown below:

$\sqrt{p}\times \frac{1}{2}\sqrt{p}=\frac{1}{2}p$

Hence, $\sqrt{p}$ is the rationalising factor of $\frac{1}{2}\sqrt{p}$.