Answer
$3$
Work Step by Step
Using $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$ or the quotient rule of radicals, the given expression, $
\dfrac{\sqrt{27x}}{\sqrt{3x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{27x}{3x}}
\\\\=
\sqrt{\dfrac{9\cdot3x}{3x}}
\\\\=
\sqrt{\dfrac{9\cdot\cancel{3x}}{\cancel{3x}}}
\\\\=
\sqrt{9}
\\\\=
\sqrt{(3)^2}
\\\\=
3
.\end{array}
Note that variables are assumed to have positive real numbers.
