Answer
$$-\dfrac{\sqrt{91}}{13}$$
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{7}{13}}&=-\dfrac{\sqrt{7}}{\sqrt{13}}\\
\end{align*}
Rationalize the denominator by multiplying $\sqrt{13}$ to both the numerator and denominator to obtain:
\begin{align*}
-\dfrac{\sqrt{7}}{\sqrt{13}} \cdot \dfrac{\sqrt{13}}{\sqrt{13}}&=-\dfrac{\sqrt{91}}{\sqrt{169}}\\\\
&=-\dfrac{\sqrt{91}}{13}
\end{align*}
