Answer
$7-\sqrt{14}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt{7}(\sqrt{7}-\sqrt{2})
,$ use the Distributive Property and the laws 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{7}(\sqrt{7})+\sqrt{7}(-\sqrt{2})
\\\\=
(\sqrt{7})^2-\sqrt{7}(\sqrt{2})
\\\\=
7-\sqrt{7}(\sqrt{2})
.\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}
7-\sqrt{7(2)}
\\\\=
7-\sqrt{14}
.\end{array}
