Answer
$5\sqrt{10}-\sqrt{30}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
