Answer
$5x\sqrt[]{3x}-6x\sqrt{5x}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[]{125x^3}-3\sqrt{20x^3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[]{25x^2\cdot3x}-3\sqrt{4x^2\cdot5x}
\\\\=
\sqrt[]{(5x)^2\cdot3x}-3\sqrt{(2x)^2\cdot5x}
\\\\=
5x\sqrt[]{3x}-3\cdot2x\sqrt{5x}
\\\\=
5x\sqrt[]{3x}-6x\sqrt{5x}
.\end{array}
Note that all variables are assumed to have positive real numbers.