Question

Simplify the expression and choose the correct answer.

$5\sqrt{12}+3\sqrt{72}-\sqrt{18}-7\sqrt{48}$

• A. $18\sqrt{3}-15\sqrt{2}$
• B. $15\sqrt{2}-18\sqrt{3}$
• C. $15\sqrt{3}-18\sqrt{2}$
• D. $12\sqrt{2}-15\sqrt{3}$

Answer 1

The correct option is B $15\sqrt{2}-18\sqrt{3}$

$5\sqrt{12}+3\sqrt{72}-\sqrt{18}-7\sqrt{48}$

$=5\sqrt{4\times 3}+3\sqrt{36\times 2}-\sqrt{9\times 2}-7\sqrt{16\times 3}$

$=5\times 2\sqrt{3}+3\times 6\sqrt{2}-3\sqrt{2}-7\times 4\sqrt{3}$

$=10\sqrt{3}+18\sqrt{2}-3\sqrt{2}-28\sqrt{3}$

$=10\sqrt{3}-28\sqrt{3}+18\sqrt{2}-3\sqrt{2}$

$=(10-28)\sqrt{3}+(18-3)\sqrt{2}$

$=(-18)\sqrt{3}+\left(15\right)\sqrt{2}$

$=15\sqrt{2}-18\sqrt{3}$