## College Algebra (6th Edition)

$5\sqrt{-8}+3\sqrt{-18}=0+19\sqrt{2}i$
$5\sqrt{-8}+3\sqrt{-18}$ Rewrite $\sqrt{-8}$ and $\sqrt{-18}$ as $(\sqrt{-1})(\sqrt{8})$ and $(\sqrt{-1})(\sqrt{18})$, respectively: $5\sqrt{-8}+3\sqrt{-18}=5(\sqrt{-1})(\sqrt{8})+3(\sqrt{-1})(\sqrt{18})=...$ Substitute $\sqrt{-1}$ by $i$: $...=5\sqrt{8}i+3\sqrt{18}i=...$ Simplify: $...=5(2)\sqrt{2}i+3(3)\sqrt{2}i=10\sqrt{2}i+9\sqrt{2}i=(10\sqrt{2}+9\sqrt{2})i=...$ $...=19\sqrt{2}i=0+19\sqrt{2}i$