Answer
$10x^2y^4z$
Work Step by Step
Given \begin{equation}
\sqrt{100 x^4 y^8 z^2}.
\end{equation} Write the radicand as a power of $2$ and take the square root.
\begin{equation}
\begin{aligned}
\sqrt{100 x^4 y^8 z^2}&=\sqrt{10^2 (x^2)^2 (y^4)^2 z^2}\\
&=\sqrt{(10x^2y^4z)^2}\\
&= 10x^2y^4z.
\end{aligned}
\end{equation} Hence $$\sqrt{100 x^4 y^8 z^2}= 10x^2y^4z.$$
