Question

Simplify the given surd: $\sqrt{12}+\sqrt{50}+5\sqrt{3}-\sqrt{147}-\sqrt{32}$.

Answer 1

The given surds can be simplified as follows:

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

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

$=(2+5-7)\sqrt{3}+(5-4)\sqrt{2}$

$=0\sqrt{3}+1\sqrt{2}$ $=\sqrt{2}$.

Hence, $\sqrt{12}+\sqrt{50}+5\sqrt{3}-\sqrt{147}-\sqrt{32}=\sqrt{2}$.