Answer
$11+4\sqrt{6}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(\sqrt{3}+\sqrt{8})^2
,$ use the special product on squaring binomials.
$\bf{\text{Solution Details:}}$
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt{3})^2+2(\sqrt{3})(\sqrt{8})+(\sqrt{8})^2
\\\\=
3+2\sqrt{3(8)}+8
\\\\=
(3+8)+2\sqrt{24}
\\\\=
11+2\sqrt{4\cdot6}
\\\\=
11+2\sqrt{(2)^2\cdot6}
\\\\=
11+2(2)\sqrt{6}
\\\\=
11+4\sqrt{6}
.\end{array}
