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: 39



Work Step by Step

Using $i=\sqrt{-1},$ $i^2=-1,$ and the properties of radicals, the given expression, $ \sqrt{-36}\sqrt{-9} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{-1}\sqrt{36}\cdot\sqrt{-1}\sqrt{9} \\\\= i\sqrt{(6)^2}\cdot i\sqrt{(3)^2} \\\\= 6i\cdot3i \\\\= 18i^2 \\\\= 18(-1) \\\\= -18 .\end{array}
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