Answer
$5\sqrt{2}+9$
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:
$=\sqrt{4(2)}+\sqrt{4^2}+\sqrt{9(2)}+\sqrt{5^2}
\\=\sqrt{2^2(2)}+4+\sqrt{3^2(2)}+5
\\=2\sqrt{2}+4+3\sqrt{2}+5$
RECALL:
For any real numbers $, a, b,$ and $c$,
$ac+bc=(a+b)c$
Use the rule above to combine like terms:
$=(2\sqrt{2}+3\sqrt{2}) + 4+5
\\=(2+3)\sqrt{2}+9
\\=5\sqrt{2}+9$
