College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding: 57

Answer

$5(\sqrt{2}+1)=5\sqrt{2}+5$

Work Step by Step

We rationalize the denominator: $\displaystyle \frac{5}{\sqrt{2}-1}=\frac{5(\sqrt{2}+1)}{(\sqrt{2}-1)(\sqrt{2}+1)}=\frac{5(\sqrt{2}+1)}{2-1}=5(\sqrt{2}+1)=5\sqrt{2}+5$
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