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 643: 76

Answer

$\frac{6-8\sqrt{30m}+3\sqrt{15}-60\sqrt{2m}}{9-480m}$.

Work Step by Step

The given expression is $=\frac{2+\sqrt{15}}{3+4\sqrt{30m}}$ Multiply and divide by the conjugate of the denominator. $=\frac{2+\sqrt{15}}{3+4\sqrt{30m}}\cdot \frac{3-4\sqrt{30m}}{3-4\sqrt{30m}}$ Use the FOIL method. $=\frac{6-8\sqrt{30m}+3\sqrt{15}+(\sqrt{15})(-4\sqrt{30m})}{9-12\sqrt{30m}+12\sqrt{30m}+(4\sqrt{30m})(-4\sqrt{30m})}$ Simplify. $=\frac{6-8\sqrt{30m}+3\sqrt{15}-60\sqrt{2m}}{9-480m}$.
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