Answer
The standard form of the expression $5\sqrt{-8}+3\sqrt{-18}$ is $0+19i\sqrt{2}$.
Work Step by Step
Consider the expression,$5\sqrt{-8}+3\sqrt{-18}$
Express all the square roots of negative numbers in terms of $i$.
$5\sqrt{-8}+3\sqrt{-18}=5i\sqrt{8}+3i\sqrt{18}$
Make the factors.
$5\sqrt{-8}+3\sqrt{-18}=5i\sqrt{4\cdot 2}+3i\sqrt{9\cdot 2}$
Use the property $\sqrt{ab}=\sqrt{a}\cdot \sqrt{b}$.
$\begin{align}
& 5\sqrt{-8}+3\sqrt{-18}=5i\sqrt{4}\cdot \sqrt{2}+3i\sqrt{9}\cdot \sqrt{2} \\
& =5i\left( 2 \right)\cdot \sqrt{2}+3i\left( 3 \right)\cdot \sqrt{2} \\
& =10i\sqrt{2}+9i\sqrt{2} \\
& =19i\sqrt{2}
\end{align}$
Express the complex number in the standard form.
$5\sqrt{-8}+3\sqrt{-18}=0+19i\sqrt{2}$
Therefore, the standard form of the expression $5\sqrt{-8}+3\sqrt{-18}$ is $0+19i\sqrt{2}$.
