Answer
$5x^2\sqrt{5}$
Work Step by Step
Using $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}},$ the given expression, $ \dfrac{15\sqrt{60x^5}}{3\sqrt{12x}} ,$ is equivalent to \begin{align*} & \dfrac{15}{3}\sqrt{\dfrac{60x^5}{12x}} \\\\&= 5\sqrt{5x^4} .\end{align*}
Extracting the perfect powers of the index, the expression above is equivalent to
\begin{align*}
&
5\sqrt{x^4\cdot5}
\\&=
5\sqrt{(x^2)^2\cdot5}
\\&=
5(x^2)\sqrt{5}
\\&=
5x^2\sqrt{5}
.\end{align*}
Hence, the simplified form of the given expression is $
5x^2\sqrt{5}
$.
