## Precalculus (6th Edition) Blitzer

The standard form of the expression $5\sqrt{-16}+3\sqrt{-81}$ is $0+47i$.
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 $0+47i$.