Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set: 23

Answer

$-2i\sqrt{19}+5i\sqrt{5}$

Work Step by Step

Using $i=\sqrt{-1}$ and the properties of radicals, the given expression, $ -\sqrt{-76}+\sqrt{-125} ,$ is equivalent to \begin{array}{l}\require{cancel} -\sqrt{76}\cdot\sqrt{-1}+\sqrt{125}\cdot\sqrt{-1} \\\\= -\sqrt{4\cdot19}\cdot i+\sqrt{25\cdot5}\cdot i \\\\= -\sqrt{(2)^2\cdot19}\cdot i+\sqrt{(5)^2\cdot5}\cdot i \\\\= -2i\sqrt{19}+5i\sqrt{5} .\end{array}
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