#### Answer

$14\sqrt{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
7(\sqrt{50}-\sqrt{18})
,$ simplify first each radical by extracting the root of the factor that is a perfect power of the index. Then combine like terms and multiply by $7$.
$\bf{\text{Solution Details:}}$
Expressing the radicand with a factor that is a perfect power of the index, the given expression is equivalent to
\begin{array}{l}\require{cancel}
7(\sqrt{25\cdot2}-\sqrt{9\cdot2})
\\\\=
7(\sqrt{(5)^2\cdot2}-\sqrt{(3)^2\cdot2})
.\end{array}
Extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
7(5\sqrt{2}-3\sqrt{2})
.\end{array}
Combining the like radicals and multiplying by $7$ result to
\begin{array}{l}\require{cancel}
7[(5-3)\sqrt{2}]
\\\\=
7[2\sqrt{2}]
\\\\=
14\sqrt{2}
.\end{array}