#### Answer

$5\sqrt{-8}+3\sqrt{-18}=0+19\sqrt{2}i$

#### Work Step by Step

$5\sqrt{-8}+3\sqrt{-18}$
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:
$...=5(2)\sqrt{2}i+3(3)\sqrt{2}i=10\sqrt{2}i+9\sqrt{2}i=(10\sqrt{2}+9\sqrt{2})i=...$
$...=19\sqrt{2}i=0+19\sqrt{2}i$