Question

What is the least rationalising factor of $\sqrt{72}$?

Answer 1

We can write $72$ as $2\times 2\times 2\times 3\times 3$

$\Rightarrow \sqrt{72}=\sqrt{2\times 2\times 2\times 3\times 3}$

$=2\times 3\sqrt{2}=6\sqrt{2}$

The rationalizing factor should be such that if we multiply it with $6\sqrt{2}$, we get a rational number.

Hence, the least rationalising factor is $\sqrt{2}$ as $6\sqrt{2}\times \sqrt{2}=12$ which is a rational number.