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: 23

Answer

$\dfrac{1}{\sqrt{12z}}=\dfrac{\sqrt{3z}}{6z}$

Work Step by Step

$\dfrac{1}{\sqrt{12z}}$ Multiply the fraction by $\dfrac{\sqrt{12z}}{\sqrt{12z}}$: $\dfrac{1}{\sqrt{12z}}\cdot\dfrac{\sqrt{12z}}{\sqrt{12z}}=\dfrac{\sqrt{12z}}{\sqrt{(12z)^{2}}}=\dfrac{\sqrt{12z}}{12z}=...$ Rewrite the expression as $\dfrac{\sqrt{4\cdot3\cdot z}}{12z}$ and simplify: $...=\dfrac{\sqrt{4\cdot3\cdot z}}{12z}=\dfrac{2\sqrt{3z}}{12z}=\dfrac{\sqrt{3z}}{6z}$
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