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 - 8.3 Multiplying and Dividing Radicals - 8.3 Exercises - Page 642: 28

Answer

$63 - 9\sqrt {35a} - 7\sqrt {10a} + 5a\sqrt {14}$

Work Step by Step

We can use the FOIL method to distribute the terms. In the FOIL method, we multiply the first terms, the outer terms, the inner terms, and then the last terms: $(9)(7) - 9\sqrt {35a} - 7\sqrt {10a} + (\sqrt {10a})(\sqrt {35a}$ Multiply to simplify: $63 - 9\sqrt {35a} - 7\sqrt {10a} + \sqrt {350a^2}$ Rewrite radicands as the product of two factors. One of the factors should be a perfect square so we can take its square root to remove it from under the radical sign: $63 - 9\sqrt {35a} - 7\sqrt {10a} + \sqrt {25 • 14 • a^2}$ Take the square root of the perfect squares: $63 - 9\sqrt {35a} - 7\sqrt {10a} + 5a\sqrt {14}$
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