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: 67

Answer

$\frac{(2\sqrt {15}+3\sqrt {5})}{120}$

Work Step by Step

Step 1: $\frac{2+\sqrt 3}{8\sqrt {15}}$ Step 2: Rationalize the denominator: $\frac{2+\sqrt 3}{8\sqrt {15}}\times\frac{8\sqrt {15}}{8\sqrt {15}}$. Step 3: $\frac{2(8\sqrt {15})+8\sqrt {15}(\sqrt 3)}{8\sqrt {15}\times8\sqrt {15}}$ Step 4: $\frac{16\sqrt {15}+8\sqrt {15\times3}}{64(15)}$ Step 5: $\frac{16\sqrt {15}+8\sqrt {15\times3}}{64(15)}$ Step 6: $\frac{16\sqrt {15}+8\sqrt {9\times5}}{64(15)}$ Step 7: $\frac{16\sqrt {15}+8(3)\sqrt {5}}{64(15)}$ Step 8: $\frac{8(2\sqrt {15}+3\sqrt {5})}{64(15)}$ Step 9: $\frac{1(2\sqrt {15}+3\sqrt {5})}{8(15)}$ Step 10: $\frac{(2\sqrt {15}+3\sqrt {5})}{120}$
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