Answer
The standard form of the expression $5\sqrt{-16}+3\sqrt{-81}$ is $0+47i$.
Work Step by Step
Consider the expression,$5\sqrt{-16}+3\sqrt{-81}$
Express all the square roots of negative numbers in terms of $i$.
$5\sqrt{-16}+3\sqrt{-81}=5i\sqrt{16}+3i\sqrt{81}$
Simplify the radicals.
$\begin{align}
& 5\sqrt{-16}+3\sqrt{-81}=5i\sqrt{{{4}^{2}}}+3i\sqrt{{{9}^{2}}} \\
& =5i\left( 4 \right)+3i\left( 9 \right) \\
& =20i+27i \\
& =47i
\end{align}$
Express the complex number in the standard form.
$5\sqrt{-16}+3\sqrt{-81}=0+47i$
Therefore, the standard form of the expression $5\sqrt{-16}+3\sqrt{-81}$ is $0+47i$.
