Answer
$6x+3\sqrt{x}-2\sqrt{5x}-\sqrt{5}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
(3\sqrt{x}-\sqrt{5})(2\sqrt{x}+1)
,$ use FOIL and the laws 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}
3\sqrt{x}(2\sqrt{x})+3\sqrt{x}(1)-\sqrt{5}(2\sqrt{x})-\sqrt{5}(1)
\\\\=
3(2)(\sqrt{x})^2+3\sqrt{x}-1(2)\sqrt{5}(\sqrt{x})-\sqrt{5}
\\\\=
6x+3\sqrt{x}-2\sqrt{5}(\sqrt{x})-\sqrt{5}
.\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}
6x+3\sqrt{x}-2\sqrt{5(x)}-\sqrt{5}
\\\\=
6x+3\sqrt{x}-2\sqrt{5x}-\sqrt{5}
.\end{array}
