Answer
$\dfrac{2\sqrt3}{3}$
Work Step by Step
Recall:
If $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers, then $\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}},$ where $a\ne0$.
Use the rule above to obtain:
\begin{align*}
\require{cancel}
\dfrac{\sqrt8}{\sqrt6}&=\sqrt{\dfrac{8}{6}}\\\\
&=\sqrt{\dfrac{\cancel{8}^4}{\cancel{6}^3}}\\\\
&=\sqrt{\dfrac{4}{3}}\\\\
&=2 \cdot \sqrt{\frac{1}{3}}
\end{align*}
Multiply $3$ to both the numerator and the denominator inside the radical sign to obtain:
\begin{align*}
2 \cdot \sqrt{\frac{1}{3} \cdot \frac{3}{3}}&=2\cdot \sqrt{\frac{3}{9}}\\\\
&=2 \cdot \sqrt{\frac{1}{9}(3)}\\\\
&=2 \cdot \sqrt{\left(\frac{1}{3}\right)^2(3)}\\\\
&=2\cdot \frac{1}{3} \sqrt3\\\\
&=\frac{2\sqrt3}{3}
\end{align*}
