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: 65

Answer

$\dfrac{2-\sqrt{11}}{6}=-\dfrac{7}{6(2+\sqrt{11})}$

Work Step by Step

$\dfrac{2-\sqrt{11}}{6}$ Multiply the numerator and the denominator of this expression by the conjugate of the numerator and simplify if possible: $\dfrac{2-\sqrt{11}}{6}=\dfrac{2-\sqrt{11}}{6}\cdot\dfrac{2+\sqrt{11}}{2+\sqrt{11}}=\dfrac{2^{2}-(\sqrt{11})^{2}}{6(2+\sqrt{11})}=...$ $...=\dfrac{4-11}{6(2+\sqrt{11})}=\dfrac{-7}{6(2+\sqrt{11})}=-\dfrac{7}{6(2+\sqrt{11})}$
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