## Intermediate Algebra (12th Edition)

$5\sqrt{10}-\sqrt{30}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $\sqrt{10}(5-\sqrt{3}) ,$ use the Distributive Property and the properties of radicals. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt{10}(5)-\sqrt{10}(\sqrt{3}) \\\\= 5\sqrt{10}-\sqrt{10}(\sqrt{3}) .\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} 5\sqrt{10}-\sqrt{10(3)} \\\\= 5\sqrt{10}-\sqrt{30} .\end{array}