Answer
$11\sqrt{2k}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To add/subtract the given expression, $
4\sqrt{18k}-\sqrt{72k}+\sqrt{50k}
,$ 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}
4\sqrt{9\cdot2k}-\sqrt{36\cdot2k}+\sqrt{25\cdot2k}
\\\\=
4\sqrt{(3)^2\cdot2k}-\sqrt{(6)^2\cdot2k}+\sqrt{(5)^2\cdot2k}
\\\\=
4(3)\sqrt{2k}-6\sqrt{2k}+5\sqrt{2k}
\\\\=
12\sqrt{2k}-6\sqrt{2k}+5\sqrt{2k}
.\end{array}
By combining the like radicals, the expression above simplifies to
\begin{array}{l}\require{cancel}
(12-6+5)\sqrt{2k}
\\\\=
11\sqrt{2k}
.\end{array}
