## Intermediate Algebra (12th Edition)

$9+4\sqrt{5}$
$\bf{\text{Solution Outline:}}$ 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}