Answer
$-3\sqrt{2k}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt{18k}-\sqrt{72k}
,$ 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{9\cdot2k}-\sqrt{36\cdot2k}
\\\\=
\sqrt{(3)^2\cdot2k}-\sqrt{(6)^2\cdot2k}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
3\sqrt{2k}-6\sqrt{2k}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(3-6)\sqrt{2k}
\\\\=
-3\sqrt{2k}
.\end{array}
