#### Answer

$9+4\sqrt{5}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
(\sqrt{5}+2)^2
,$ use the special product on squaring binomials and the properties of radicals. Then combine like terms.
$\bf{\text{Solution Details:}}$
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{5})^2+2(\sqrt{5})(2)+(2)^2
\\\\=
5+4\sqrt{5}+4
.\end{array}
By combining like terms, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(5+4)+4\sqrt{5}
\\\\=
9+4\sqrt{5}
.\end{array}