Answer
$15x^2$
Work Step by Step
Using $\sqrt[n]{x}\cdot\sqrt[n]{y}=\sqrt[n]{xy},$ the given expression, $
\sqrt[]{9x^2}\cdot\sqrt[]{25x^2}
,$ is equivalent to
\begin{align*}
&
\sqrt[]{9x^2(25x^2)}
\\&=
\sqrt[]{225x^4}
.\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[]{(15x^2)^2}
\\&=
15x^2
.\end{align*}
Hence, the simplified form of the given expression is $
15x^2
$.
