Answer
$13\sqrt{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
5\sqrt{8}+3\sqrt{72}-3\sqrt{50}
,$ 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}
5\sqrt{4\cdot2}+3\sqrt{36\cdot2}-3\sqrt{25\cdot2}
\\\\=
5\sqrt{(2)^2\cdot2}+3\sqrt{(6)^2\cdot2}-3\sqrt{(5)^2\cdot2}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
5(2)\sqrt{2}+3(6)\sqrt{2}-3(5)\sqrt{2}
\\\\=
10\sqrt{2}+18\sqrt{2}-15\sqrt{2}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(10+18-15)\sqrt{2}
\\\\=
13\sqrt{2}
.\end{array}
