#### Answer

$x+8\sqrt{x-3}+13$

#### Work Step by Step

Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, and the properties of radicals, the given expression, $
(4+\sqrt{x-3})^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(4)^2+2(4)(\sqrt{x-3})+(\sqrt{x-3})^2
\\\\=
16+8\sqrt{x-3}+x-3
\\\\=
x+8\sqrt{x-3}+(-3+16)
\\\\=
x+8\sqrt{x-3}+13
.\end{array}