Answer
$4\sqrt{2x}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt{72x}-\sqrt{8x}
,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals.
$\bf{\text{Solution Details:}}$
Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt{36\cdot2x}-\sqrt{4\cdot2x}
\\\\=
\sqrt{(6)^2\cdot2x}-\sqrt{(2)^2\cdot2x}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
6\sqrt{2x}-2\sqrt{2x}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(6-2)\sqrt{2x}
\\\\=
4\sqrt{2x}
.\end{array}
