Question

Simplify the given surd $4\sqrt{12}-\sqrt{50}-7\sqrt{48}$.

Answer 1

The given surds can be simplified as follows:

$4\sqrt{12}-\sqrt{50}-7\sqrt{48}=4\sqrt{4\times 3}-\sqrt{25\times 2}-7\sqrt{16\times 3}=(4\times 2\sqrt{3})-5\sqrt{2}-(7\times 4\sqrt{3})=8\sqrt{3}-5\sqrt{2}-28\sqrt{3}$

$=\sqrt{3}(8-28)-5\sqrt{2}=-20\sqrt{3}-5\sqrt{2}$

Hence, $4\sqrt{12}-\sqrt{50}-7\sqrt{48}=-20\sqrt{3}-5\sqrt{2}$.