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: 6

Answer

$5i\sqrt{5}$

Work Step by Step

Factor the radicand so that one factor $-1$ to obtain: $=\sqrt{125(-1)} \\=\sqrt{25(5)(-1)} \\=\sqrt{5^2(5)(-1)}$ RECALL: (1) $\sqrt{abc} = \sqrt{a} \cdot \sqrt{b} \cdot \sqrt{c}$ (2) $\sqrt{-1} = i$ Use rule (1) above to obtain: $=\sqrt{5^2} \cdot \sqrt{5} \cdot \sqrt{-1} \\=5 \cdot \sqrt{5} \cdot \sqrt{-1} \\=5\sqrt{5} \cdot \sqrt{-1}$ Use rule (2) above to obtain: $=5\sqrt{5} \cdot i \\=5i\sqrt{5}$
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