Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.1 - Complex Numbers - Exercise Set - Page 315: 56


The standard form of the expression $5\sqrt{-8}+3\sqrt{-18}$ is $0+19i\sqrt{2}$.

Work Step by Step

Consider the expression,$5\sqrt{-8}+3\sqrt{-18}$ Express all the square roots of negative numbers in terms of $i$. $5\sqrt{-8}+3\sqrt{-18}=5i\sqrt{8}+3i\sqrt{18}$ Make the factors. $5\sqrt{-8}+3\sqrt{-18}=5i\sqrt{4\cdot 2}+3i\sqrt{9\cdot 2}$ Use the property $\sqrt{ab}=\sqrt{a}\cdot \sqrt{b}$. $\begin{align} & 5\sqrt{-8}+3\sqrt{-18}=5i\sqrt{4}\cdot \sqrt{2}+3i\sqrt{9}\cdot \sqrt{2} \\ & =5i\left( 2 \right)\cdot \sqrt{2}+3i\left( 3 \right)\cdot \sqrt{2} \\ & =10i\sqrt{2}+9i\sqrt{2} \\ & =19i\sqrt{2} \end{align}$ Express the complex number in the standard form. $5\sqrt{-8}+3\sqrt{-18}=0+19i\sqrt{2}$ Therefore, the standard form of the expression $5\sqrt{-8}+3\sqrt{-18}$ is $0+19i\sqrt{2}$.
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