Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Test - Page 578: 20


$-5 + 2\sqrt 6$

Work Step by Step

Simplify. $\dfrac{\sqrt 2 -\sqrt 3}{\sqrt 2+\sqrt3}$ Now, $\dfrac{\sqrt 2 -\sqrt 3}{\sqrt 2+\sqrt3}=\dfrac{\sqrt 2 -\sqrt 3}{\sqrt 2+\sqrt3} \cdot \dfrac{\sqrt 2 -\sqrt 3}{\sqrt 2-\sqrt3}$ or, $=\dfrac{2+3-2\sqrt 2 \sqrt 3}{(\sqrt 2)^2-(\sqrt3)^2}$ or, $=\dfrac{{5 -2\sqrt 6}}{-1}$ we have $=-5 + 2\sqrt 6$
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