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: 43

Answer

$-3\sqrt{14}$

Work Step by Step

Using $i=\sqrt{-1},$ $i^2=-1,$ and the properties of radicals, the given expression, $ \sqrt{-6}\sqrt{-21} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{-1}\sqrt{6}\cdot\sqrt{-1}\sqrt{21} \\\\= i\sqrt{6}\cdot i\sqrt{21} \\\\= i(i)\sqrt{6(21)} \\\\= i^2\sqrt{(3\cdot2)(3\cdot7)} \\\\= i^2\sqrt{(3)^2\cdot14} \\\\= 3i^2\sqrt{14} \\\\= 3(-1)\sqrt{14} \\\\= -3\sqrt{14} .\end{array}
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