Answer
$\dfrac{\sqrt{15x}}{5x}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\sqrt{\dfrac{3}{5x}}
,$ multiply the radicand by an expression equal to $1$ which will make the denominator a perfect power of the index. Then use the laws of radicals to simplify the result
$\bf{\text{Solution Details:}}$
Multiplying the radicand by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{3}{5x}\cdot\dfrac{5x}{5x}}
\\\\=
\sqrt{\dfrac{15x}{(5x)^2}}
.\end{array}
Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{15x}}{\sqrt{(5x)^2}}
\\\\=
\dfrac{\sqrt{15x}}{5x}
.\end{array}