Question

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

• A. $\sqrt{2}$
• B. $\sqrt{7}$
• C. $\sqrt{3}$
• D. $\sqrt{5}$

Answer 1

Answer: (A)

$\sqrt{2}$

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.