Question

What is the least rationalizing factor of $\sqrt{24}$?

• A. $\sqrt{24}$
• B. $\sqrt{2}$
• C. $\sqrt{3}$
• D. $\sqrt{6}$

Answer 1

The correct option is D

$\sqrt{6}$

We can write $24$ as $2\times 2\times 2\times 3$.

$\Rightarrow \sqrt{24}=\sqrt{2\times 2\times 2\times 3}$

$=2\sqrt{6}$

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

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