# Chapter 1 - Equations and Inequalities - Exercise Set 1.4 - Page 142: 32

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

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

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