Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.5 - Multiplying and Dividing Radical Expressions - 7.5 Exercises: 109

Answer

$\dfrac{p\sqrt{p+2}}{p+2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To rationalize the denominator of the given expression, $ \dfrac{p}{\sqrt{p+2}} ,$ multiply both the numerator and the denominator by the denominator. $\bf{\text{Solution Details:}}$ Multiplying both the numerator and the denominator by the denominator, the given expression is equivalent to \begin{array}{l}\require{cancel} \dfrac{p}{\sqrt{p+2}}\cdot\dfrac{\sqrt{p+2}}{\sqrt{p+2}} \\\\= \dfrac{p\sqrt{p+2}}{(\sqrt{p+2})^2} \\\\= \dfrac{p\sqrt{p+2}}{p+2} .\end{array}
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