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: 54

Answer

$\displaystyle \frac{\sqrt{2}(\sqrt{7}-2)}{3}=\frac{\sqrt{14}-2\sqrt{2}}{3}$

Work Step by Step

We rationalize the denominator: $\displaystyle \frac{\sqrt{2}}{\sqrt{7}+2}=\frac{\sqrt{2}(\sqrt{7}-2)}{(\sqrt{7}+2)(\sqrt{7}-2)}=\frac{\sqrt{2}(\sqrt{7}-2)}{7-4}=\frac{\sqrt{2}(\sqrt{7}-2)}{3}=\frac{\sqrt{14}-2\sqrt{2}}{3}$
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