Answer
$\left(\sqrt{5}+2\sqrt{6} \right)i\approx 7.135i$
Work Step by Step
Given \begin{equation}
\sqrt{-5}+\sqrt{-24}.
\end{equation} Replace the square root of negative $1$ by $i$.
\begin{equation}
\begin{aligned}
\sqrt{-5}+\sqrt{-24}&=\sqrt{-1}\cdot \sqrt{5}+ \sqrt{-1}\cdot \sqrt{24}\\
& = \left(\sqrt{5}+\sqrt{24} \right)\sqrt{-1}\\
&=\left(\sqrt{5}+2\sqrt{6} \right)i\\
&\approx 7.135i.
\end{aligned}
\end{equation} The solution is $$\left(\sqrt{5}+2\sqrt{6} \right)i\approx 7.135i. $$
