#### Answer

$-\dfrac{\sqrt{39}}{15}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
-\sqrt{\dfrac{13}{75}}
,$ multiply both the numerator and the denominator by an expression that will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Converting the radicand as an expression that contains a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
-\sqrt{\dfrac{13}{25\cdot3}}
\\\\=
-\sqrt{\dfrac{13}{(5)^2\cdot3}}
.\end{array}
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{13}{(5)^2\cdot3}\cdot\dfrac{3}{3}}
\\\\=
-\sqrt{\dfrac{39}{(5)^2\cdot3^2}}
.\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{39}}{\sqrt{(5)^2\cdot3^2}}
\\\\=
-\dfrac{\sqrt{39}}{5\cdot3}
\\\\=
-\dfrac{\sqrt{39}}{15}
.\end{array}