Answer
The standard form of the expression $\frac{4+\sqrt{-8}}{2}$ is $2+i\sqrt{2}$.
Work Step by Step
Consider the expression,
$\frac{4+\sqrt{-8}}{2}$
Rewrite the expression $\frac{4+\sqrt{-8}}{2}$ as $\frac{4+\sqrt{8}\sqrt{-1}}{2}$
As $\sqrt{-1}=i$
Therefore,
$\frac{4+\sqrt{8}\sqrt{-1}}{2}=\frac{4+2i\sqrt{2}}{2}$
Simplify the above expression.
$\begin{align}
& \frac{4+2i\sqrt{2}}{2}=\frac{2\left( 2+i\sqrt{2} \right)}{2} \\
& =2+i\sqrt{2}
\end{align}$
Hence, the standard form of the expression $\frac{4+\sqrt{-8}}{2}$ is $2+i\sqrt{2}$.
