Answer
$\dfrac{10}{3}$
Work Step by Step
Using $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$ or the quotient rule of radicals, the given expression, $
\sqrt{\dfrac{100}{9}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{100}}{\sqrt{9}}
\\\\=
\dfrac{\sqrt{(10)^2}}{\sqrt{(3)^2}}
\\\\=
\dfrac{10}{3}
.\end{array}
Note that variables are assumed to have positive real numbers.
