Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Review: 130

Answer

$-\sqrt {10}$

Work Step by Step

$\sqrt {-2}\times\sqrt {-5}$ =$\sqrt {-1\times2}\times\sqrt {-1\times5}$ =$(\sqrt {-1}\times\sqrt {2})\times(\sqrt {-1}\times\sqrt {5})$ =$(i\times\sqrt {2})\times(i\times\sqrt {5})$ =$(i\sqrt {2})\times(i\sqrt {5})$ =$i\times i \times\sqrt 2\times\sqrt 5$ =$i^{2}\times\sqrt {2\times5}$ =$i^{2}\times\sqrt {10}$ =$(-1)\times\sqrt {10}$ =$-\sqrt {10}$
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