Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set: 62

Answer

$-3\sqrt{5}$

Work Step by Step

RECALL: (1) $\sqrt{-1}=i$ (2) $i^2=-1$ (3) $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$ Simplify each radical by using rules (1) and (3) above: $=\sqrt{9(-1)} \cdot \sqrt{5(-1)} \\=\sqrt{3^2(-1)} \cdot (\sqrt{5} \cdot \sqrt{-1}) \\=3\sqrt{-1} \cdot (\sqrt{5} \cdot i) \\=3i \cdot i\sqrt{5} \\=3i^2\sqrt{5}$ Use rule (2) above to obtain: $=3(-1)\sqrt{5} \\=-3\sqrt{5}$
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