Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.5 - Rationalizing Denominators and Numerators of Radical Expressions - Exercise Set - Page 445: 49

Answer

$-\dfrac{8-8\sqrt{10}}{9}$

Work Step by Step

Rationalizing the denominator of $ \dfrac{8}{1+\sqrt{10}} $ results to \begin{array}{l} \dfrac{8}{1+\sqrt{10}} \cdot \dfrac{1-\sqrt{10}}{1-\sqrt{10}} \\\\= \dfrac{8-8\sqrt{10}}{(1)^2-(\sqrt{10})^2} \\\\= \dfrac{8-8\sqrt{10}}{1-10} \\\\= \dfrac{8-8\sqrt{10}}{-9} \\\\= -\dfrac{8-8\sqrt{10}}{9} .\end{array}
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