Question

The simplest rationalizing factor of $\sqrt{75}$ is.

• A. $(75{)}^{1/3}$
• B. $5\sqrt{3}$
• C. $3$
• D. $\sqrt{150}$

Answer 1

Answer: (B)

$5\sqrt{3}$

Let us first factorize $75$ as shown below:

$75=3\times 5\times 5=3\times 5^2$

Now consider $\sqrt{75}$ as follows:

$\sqrt{75}=\sqrt{3\times 5\times 5}=\sqrt{3\times 5^2}=\sqrt{3}\times \sqrt{5^2}=5\sqrt{3}$

Hence, the simplest rationalizing factor of $\sqrt{75}$ is $5\sqrt{3}$.