Answer
$\dfrac{5\sqrt[]{x}}{2}$
Work Step by Step
Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[]{75x}}{2\sqrt[]{3}}
\\\\=
\dfrac{1}{2}\cdot\sqrt[]{\dfrac{75x}{3}}
\\\\=
\dfrac{1}{2}\cdot\sqrt[]{25x}
\\\\=
\dfrac{\sqrt[]{25x}}{2}
.\end{array}
Extracting the factors that are perfect powers of the index, the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[]{25x}}{2}
\\\\=
\dfrac{\sqrt[]{(5)^2\cdot x}}{2}
\\\\=
\dfrac{5\sqrt[]{x}}{2}
.\end{array}
