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 - Exercise Set: 39

Answer

$\dfrac{8}{1+\sqrt{10}}=-\dfrac{8(1-\sqrt{10})}{9}$

Work Step by Step

$\dfrac{8}{1+\sqrt{10}}$ Multiply the numerator and the denominator of this expression by the conjugate of the denominator and simplify if possible: $\dfrac{8}{1+\sqrt{10}}=\dfrac{8}{1+\sqrt{10}}\cdot\dfrac{1-\sqrt{10}}{1-\sqrt{10}}=\dfrac{8(1-\sqrt{10})}{1^{2}-(\sqrt{10})^{2}}=...$ $...=\dfrac{8(1-\sqrt{10})}{1-10}=\dfrac{8(1-\sqrt{10})}{-9}=-\dfrac{8(1-\sqrt{10})}{9}$
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