Answer
$$\dfrac{\sqrt{5}}{5}$$
Work Step by Step
RECALL:
(1) For any real numbers $a \ge 0, b\ge0$, $\sqrt{ab}=\sqrt{a} \cdot \sqrt{b}$
(2) For any real numbers $a \ge 0, b\gt 0$, $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$
Use rule (2) above to obtain:
\begin{align*}
\sqrt{\dfrac{3}{15}}&=\dfrac{\sqrt{3}}{\sqrt{15}}\\
\end{align*}
Rationalize the denominator by multiplying $\sqrt{15}$ to both the numerator and denominator to obtain:
\begin{align*}
\dfrac{\sqrt{3}}{\sqrt{15}} \cdot \dfrac{\sqrt{15}}{\sqrt{15}}&=\dfrac{\sqrt{45}}{\sqrt{225}}\\\\
&=\dfrac{\sqrt{45}}{15}\\\\
&=\dfrac{\sqrt{9(5)}}{15}\\\\
&=\dfrac{\sqrt9 \cdot \sqrt5}{15}\\\\
&=\dfrac{3\sqrt5}{15}
\end{align*}
Cancel the common factor $3$ to obtain:
\begin{align*}
\require{cancel}
\dfrac{3\sqrt5}{15}&=\dfrac{\cancel{3}\sqrt5}{\cancel{15}^5}\\\\
&=\dfrac{\sqrt5}{5}
\end{align*}
