Answer
$-\dfrac{3}{4}$
Work Step by Step
Using the properties of radicals, the given expression, $
-\sqrt{\dfrac{81}{144}}
,$ simplifies to
\begin{array}{l}
-\sqrt{ \left( \dfrac{9}{12} \right)^2}
\\\\=
-\dfrac{9}{12}
\\\\=
-\dfrac{3}{4}
.\end{array}