Answer
$3\sqrt{2}+8$
Work Step by Step
Simplify the radicals that can still be simplified by factoring the radicand so that one of the factors is a perfect square:
$=\sqrt{6}+\sqrt{3^2}+\sqrt{4(6)}+\sqrt{5^2}
\\=\sqrt{6}+3+\sqrt{2^2(6)}+5
\\=\sqrt{6}+3+2\sqrt{6}+5$
RECALL:
For any real numbers $, a, b,$ and $c$,
$ac+bc=(a+b)c$
Use the rule above to combine like terms:
$=(\sqrt{6}+2\sqrt{6}) + 3+5
\\=(1+2)\sqrt{2}+8
\\=3\sqrt{2}+8$
