Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.4 - Imaginary Numbers as Solutions of Quadratic Equations - Exercise Set: 7

Answer

$2i\sqrt{5}$

Work Step by Step

Using the properties of radicals and that $i=\sqrt{-1}$, then the given expression, $ \sqrt{-20} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{-1}\cdot\sqrt{20} \\\\= i\cdot\sqrt{4\cdot5} \\\\= i\cdot\sqrt{(2)^2\cdot5} \\\\= i\cdot2\sqrt{5} \\\\= 2i\sqrt{5} .\end{array}
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