Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 1 - 1.5 - Complex Numbers - 1.5 Exercises - Page 120: 81


$(\sqrt {-72})^3=-432\sqrt 2i$

Work Step by Step

Use: $i^2=-1$ and $\sqrt {-1}=i$ $(\sqrt {-72})^3=(\sqrt {72}\sqrt {-1})^3=(6\sqrt 2i)^3=(6\sqrt 2)^3i^3=6^3(\sqrt 2)^3(i^2)i=216(2\sqrt 2)(-1)i=-432\sqrt 2i$
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