Answer
$\dfrac{\sqrt[]{15x}}{10}$
Work Step by Step
Rationalizing the denominator of the given expression, $
\sqrt[]{\dfrac{3x}{20}}
,$ we find:
\begin{array}{l}\require{cancel}
\sqrt[]{\dfrac{3x}{20}\cdot\dfrac{5}{5}}
\\\\=
\sqrt[]{\dfrac{15x}{100}}
\\\\=
\dfrac{\sqrt[]{15x}}{\sqrt[]{100}}
\\\\=
\dfrac{\sqrt[]{15x}}{\sqrt[]{(10)^2}}
\\\\=
\dfrac{\sqrt[]{15x}}{10}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.