Answer
$49+12\sqrt{13}$
Work Step by Step
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 given expression, $
(\sqrt{13}+6)^2
,$ is equivalent to
\begin{align*}
&
(\sqrt{13})^2+2(\sqrt{13})(6)+(6)^2
\\&=
13+12\sqrt{13}+36
\\&=
(13+36)+12\sqrt{13}
\\&=
49+12\sqrt{13}
.\end{align*}
Hence, the product of the given expression is $
49+12\sqrt{13}
$.
