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: 61

Answer

$\sqrt{\dfrac{18x^{4}y^{6}}{3z}}=\dfrac{6x^{2}y^{3}}{\sqrt{6z}}$

Work Step by Step

$\sqrt{\dfrac{18x^{4}y^{6}}{3z}}$ Rewrite this expression as $\dfrac{\sqrt{9\cdot2(x^{4}y^6)}}{\sqrt{3z}}$ and simplify it: $\sqrt{\dfrac{18x^{4}y^{6}}{3z}}=\dfrac{\sqrt{9\cdot2(x^{4}y^6)}}{\sqrt{3z}}=\dfrac{3x^{2}y^{3}\sqrt{2}}{\sqrt{3z}}=...$ Multiply this fraction by $\dfrac{\sqrt{2}}{\sqrt{2}}$ and simplify again if possible: $...=\dfrac{3x^{2}y^{3}\sqrt{2}}{\sqrt{3z}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{3x^{2}y^{3}\sqrt{2^{2}}}{\sqrt{6z}}=\dfrac{3x^{2}y^{3}(2)}{\sqrt{6z}}=\dfrac{6x^{2}y^{3}}{\sqrt{6z}}$
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