Answer
$\sqrt{15}-2\sqrt{3}+3\sqrt{5}-6$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
(\sqrt{3}+3)(\sqrt{5}-2)
,$ use FOIL and the properties of radicals.
$\bf{\text{Solution Details:}}$
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\sqrt{3}(\sqrt{5})-\sqrt{3}(2)+3(\sqrt{5})+3(-2)
\\\\=
\sqrt{3}(\sqrt{5})-2\sqrt{3}+3\sqrt{5}-6
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\sqrt{3(5)}-2\sqrt{3}+3\sqrt{5}-6
\\\\=
\sqrt{15}-2\sqrt{3}+3\sqrt{5}-6
.\end{array}
