Answer
$20\sqrt{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
5(\sqrt{72}-\sqrt{8})
,$ 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 $5$.
$\bf{\text{Solution Details:}}$
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}
5(\sqrt{36\cdot2}-\sqrt{4\cdot2})
\\\\=
5(\sqrt{(6)^2\cdot2}-\sqrt{(2)^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}
5(6\sqrt{2}-2\sqrt{2})
.\end{array}
Combining the like radicals results to
\begin{array}{l}\require{cancel}
5[(6-2)\sqrt{2}]
\\\\=
5[4\sqrt{2}]
\\\\=
20\sqrt{2}
.\end{array}
