Answer
$x\sqrt[]{15}$
Work Step by Step
Using $\sqrt[n]{x}\cdot\sqrt[n]{y}=\sqrt[n]{xy},$ the given expression, $
\sqrt[]{3x}\cdot\sqrt[]{5x}
,$ is equivalent to
\begin{align*}
&
\sqrt[]{3x(5x)}
\\&=
\sqrt[]{15x^2}
.\end{align*}
Extracting the root of the factors that is a perfect power of the index, the expression above is equivalent to
\begin{align*}
&
\sqrt[]{x^2\cdot15}
\\&=
x\sqrt[]{15}
.\end{align*}
Hence, the simplified form of the given expression is $
x\sqrt[]{15}
$.
