Question

The value of $2\sqrt{3}-3\sqrt{12}+5\sqrt{75}$ is equal to:

• A. $4\sqrt{3}$
• B. $7\sqrt{5}$
• C. $3\sqrt{5}$
• D. $21\sqrt{3}$

Answer 1

Answer: (D)

$21\sqrt{3}$

$2\sqrt{3}-3\sqrt{12}+5\sqrt{75}$
$=2\sqrt{3}-3\sqrt{3\times 2\times 2}+5\sqrt{5\times 5\times 3}$
$=2\sqrt{3}-6\sqrt{3}+25\sqrt{3}$
$=\sqrt{3}(2-6+25)$
$=\sqrt{3}\left(21\right)=21\sqrt{3}$.

Therefore, option $D$ is correct.