Answer
$20\sqrt{2}-5\sqrt{3}$
Work Step by Step
Simplify each radical to obtain
$3\sqrt{4(2)} -\sqrt{16(2)}+3\sqrt{36(2)}-\sqrt{25(3)}
\\=3\sqrt{2^2(2)} -\sqrt{4^2(2)}+3\sqrt{6^2(2)}-\sqrt{5^2(3)}
\\=3\cdot2\sqrt{2} -4\sqrt{2}+3\cdot6\sqrt{2}-5\sqrt{3)}
\\=6\sqrt{2}-4\sqrt{2}+18\sqrt{2}-5\sqrt{3}.$
RECALL:
The distributive property states that for any real numbers a, b, and c,
$(ac-bc)=(a-b)c.$
Use the rule above to obtain
$(6-4+18)\sqrt{2}-5\sqrt{3}
\\=20\sqrt{2}-5\sqrt{3}.$
