Answer
$3x\sqrt{10}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of radicals to simplify the given expression, $
\sqrt{6x}\sqrt{15x}
.$
$\bf{\text{Solution Details:}}$
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{6x}\sqrt{15x}
\\\\=
\sqrt{6x(15x)}
\\\\=
\sqrt{90x^2}
.\end{array}
Extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt{90x^2}
\\\\=
\sqrt{9x^2\cdot10}
\\\\=
\sqrt{(3x)^2\cdot10}
\\\\=
3x\sqrt{10}
.\end{array}
Note that it is assumed that radicands were not formed by raising negative numbers to even powers.
