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 - Page 686: 44



Work Step by Step

Using $i=\sqrt{-1},$ $i^2=-1,$ and the properties of radicals, the given expression, $ \sqrt{-15}\sqrt{-10} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{-1}\sqrt{15}\cdot\sqrt{-1}\sqrt{10} \\\\= i\sqrt{15}\cdot i\sqrt{10} \\\\= i(i)\sqrt{15(10)} \\\\= i^2\sqrt{(3\cdot5)(2\cdot5)} \\\\= i^2\sqrt{(5)^2\cdot6} \\\\= 5i^2\sqrt{6} \\\\= 5(-1)\sqrt{6} \\\\= -5\sqrt{6} .\end{array}
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