College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding: 50

Answer

$3i$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ \sqrt{-9} ,$ use the properties of radicals and the equivalence $i=\sqrt{-1}.$ $\bf{\text{Solution Details:}}$ Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel} \sqrt{-1}\cdot\sqrt{9} .\end{array} Since $i=\sqrt{-1},$ the expression above is equivalent to \begin{array}{l}\require{cancel} i\sqrt{9} .\end{array} Extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} i\sqrt{(3)^2} \\\\= i(3) \\\\= 3i .\end{array}
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