Answer
$16\sqrt{2}$
Work Step by Step
The geometric sequence is $2,2\sqrt{2},4,...$.
The common ratio is,
$\begin{align}
& r=\frac{{{a}_{2}}}{{{a}_{1}}} \\
& =\frac{2\sqrt{2}}{2} \\
& =\sqrt{2}
\end{align}$
So,
$r=\sqrt{2}$
$\begin{align}
& {{a}_{8}}=2{{\left( \sqrt{2} \right)}^{8-1}} \\
& =2{{\left( \sqrt{2} \right)}^{7}}
\end{align}$
Therefore,
$\begin{align}
& {{a}_{10}}=2{{\left( \sqrt{2} \right)}^{8-1}} \\
& =16\sqrt{2}
\end{align}$
Thus, the $8\text{th}$ term of the geometric sequence $\sqrt{3},3,3\sqrt{3},...$ is$16\sqrt{2}$.
