Answer
$9\sqrt{2}+8\sqrt{3}$
Work Step by Step
Factor the radicands so that one of the factors is a perfect square:
$=4\sqrt{4(2)}-\sqrt{64(2)}+2\sqrt{16(3)}+3\sqrt{9(2)}
\\=4\sqrt{2^2(2)}-\sqrt{8^2(2)}+2\sqrt{4^2(3)}+3\sqrt{3^2(2)}$
Simplify to obtain:
$\\=4\cdot 2\sqrt{2}-8\sqrt{2}+2\cdot 2\sqrt{3}+3\cdot 3\sqrt{2}
\\=8\sqrt{2}-8\sqrt{2}+8\sqrt{3}+9\sqrt{2}$
Combine like terms:
$=(8\sqrt{2} - 8\sqrt{2}+9\sqrt{2}) + 8\sqrt{3}
\\=(8-8+9)\sqrt{2} + 8\sqrt{3}
\\=9\sqrt{2}+8\sqrt{3}$
