Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Practice: 7

Answer

$\frac{\sqrt {15}+\sqrt {10}+3\sqrt 3+3\sqrt 2}{1}$

Work Step by Step

$\frac{\sqrt 5+3}{\sqrt 3-\sqrt 2}\times\frac{\sqrt 3+\sqrt 2}{\sqrt 3+\sqrt 2}$ =$\frac{(\sqrt 5+3)\times(\sqrt 3+\sqrt 2)}{(\sqrt 3+\sqrt 2)(\sqrt 3-\sqrt 2)}$ =$\frac{\sqrt 5(\sqrt 3+\sqrt 2)+3(\sqrt 3+\sqrt 2)}{(\sqrt 3)^{2}-(\sqrt 2)^{2}}$ =$\frac{\sqrt {15}+\sqrt {10}+3\sqrt 3+3\sqrt 2}{3-2}$ =$\frac{\sqrt {15}+\sqrt {10}+3\sqrt 3+3\sqrt 2}{1}$
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