Answer
$$4$$
Work Step by Step
RECALL:
(1) For $a\gt 0, b \gt0$, $\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$.
(2) If $n$ is odd, $\sqrt[n]{a^n} = a$.
(3) If $n$ is even, $\sqrt[n]{a^n} = |a|$.
Using rule (1) above gives:
\begin{align*}
\sqrt2 \cdot \sqrt8&=\sqrt{2(8)}\\
&=\sqrt{16}\\
&=\sqrt{4(4)}\\
&=\sqrt{4^2}\\
\end{align*}
Use rule (3) above to obtain:
\begin{align*}
\sqrt{4^2}&=|4|\\
&=4
\end{align*}
