Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 8 - Radical Functions - Chapter Review Exercises: 78

Answer

$(6+5\sqrt {2})+(-2\sqrt {10}+3\sqrt {5})i$

Work Step by Step

$(2+\sqrt {-5})(3-\sqrt {-10})$ $=2(3-\sqrt {-10})+\sqrt {-5}(3-\sqrt {-10})$ $=6-2\sqrt {-10}+3\sqrt {-5}-\sqrt {-5}\sqrt {-10}$ $=6-2\sqrt {-1\times10}+3\sqrt {-1\times5}-i^{2}\sqrt {5\times10}$ $=6-2i\sqrt {10}+3i\sqrt {5}-(-1)\sqrt {50}$ $=6-2i\sqrt {10}+3i\sqrt {5}+\sqrt {2\times25}$ $=6-2i\sqrt {10}+3i\sqrt {5}+5\sqrt {2}$ $=(6+5\sqrt {2})+(-2\sqrt {10}+3\sqrt {5})i$
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