Answer
$12\sqrt{2x}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To add/subtract the given expression, $
8\sqrt{2x}-\sqrt{8x}+\sqrt{72x}
,$ simplify first each radical term by extracting the factor that is a perfect power of the index. Then, combine the like radicals.
$\bf{\text{Solution Details:}}$
Extracting the factors of each radicand that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
8\sqrt{2x}-\sqrt{4\cdot2x}+\sqrt{36\cdot2x}
\\\\=
8\sqrt{2x}-\sqrt{(2)^2\cdot2x}+\sqrt{(6)^2\cdot2x}
\\\\=
8\sqrt{2x}-2\sqrt{2x}+6\sqrt{2x}
.\end{array}
By combining the like radicals, the expression above simplifies to
\begin{array}{l}\require{cancel}
(8-2+6)\sqrt{2x}
\\\\=
12\sqrt{2x}
.\end{array}
