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: 68

Answer

$\frac{(4\sqrt {10}+5\sqrt {2})}{70}$

Work Step by Step

Step 1: $\frac{4+\sqrt 5}{7\sqrt {10}}$ Step 2: Rationalize the denominator: $\frac{4+\sqrt 5}{7\sqrt {10}}\times\frac{7\sqrt {10}}{7\sqrt {10}}$. Step 3: $\frac{4(7\sqrt {10})+7\sqrt {10}(\sqrt 5)}{7\sqrt {10}\times7\sqrt {10}}$ Step 4: $\frac{28\sqrt {10}+7\sqrt {10\times5}}{49(10)}$ Step 5: $\frac{28\sqrt {10}+7\sqrt {25\times2}}{49(10)}$ Step 6: $\frac{28\sqrt {10}+7(5)\sqrt {2}}{49(10)}$ Step 8: $\frac{7(4\sqrt {10}+5\sqrt {2})}{49(10)}$ Step 9: $\frac{1(4\sqrt {10}+5\sqrt {2})}{7(10)}$ Step 10: $\frac{(4\sqrt {10}+5\sqrt {2})}{70}$
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