Question

Simplify: square root of 108 - 3 square root of 50 + 5 square root of 12 + 4 square root of 18

Answer 1

First try factoring all the radicands.

Answer 2

\[\sqrt{108}-3\sqrt{50}+5\sqrt{12}+4\sqrt{18}=\]\[\sqrt{108}=\sqrt{36\times3}=6\sqrt{3}\]\[-3\sqrt{50}=-3\sqrt{25\times2}=-15\sqrt{2}\]\[5\sqrt{12}=5\sqrt{4\times3}=10\sqrt{3}\]\[4\sqrt{18}=4\sqrt{9\times2}=12\sqrt{2}\] Now you can combine them and simplify further.

Answer 3

Just from inspection it looks like; \[16\sqrt{3}-3\sqrt{2}\]