Answer
$\color{blue}{11+4\sqrt6}$
Work Step by Step
RECALL:
$(a+b)^2=a^2+2ab+b^2$
Use the formula above with $a=\sqrt3$ and $b=\sqrt8$ to obtain:
$(\sqrt3+\sqrt8)^2
\\=(\sqrt3)^2+2(\sqrt3)(\sqrt8) + (\sqrt8)^2
\\=3 + 2\sqrt{3\cdot8}+8
\\=11 + 2\sqrt{24}$
Factor the radicand so that one factor is a perfect square, then bring out the square root of the perfect square factor to obtain:
$=11+2\sqrt{4(6)}
\\=11+2(2)\sqrt6
\\=\color{blue}{11+4\sqrt6}$
