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: 62

Answer

$\sqrt{\dfrac{8x^{5}y}{2z}}=\dfrac{2x^{3}y}{\sqrt{xyz}}$

Work Step by Step

$\sqrt{\dfrac{8x^{5}y}{2z}}$ Rewrite this expression as $\dfrac{\sqrt{4\cdot2(x^{5}y)}}{\sqrt{2z}}$ and simplify it: $\sqrt{\dfrac{8x^{5}y}{2z}}=\dfrac{\sqrt{4\cdot2(x^{5}y)}}{\sqrt{2z}}=\dfrac{2x^{2}\sqrt{2xy}}{\sqrt{2z}}=...$ Multiply the fraction by $\dfrac{\sqrt{2xy}}{\sqrt{2xy}}$ and simplify again if possible: $...=\dfrac{2x^{2}\sqrt{2xy}}{\sqrt{2z}}\cdot\dfrac{\sqrt{2xy}}{\sqrt{2xy}}=\dfrac{2x^{2}\sqrt{(2xy)^{2}}}{\sqrt{4xyz}}=\dfrac{2x^{2}(2xy)}{2\sqrt{xyz}}=...$ $...=\dfrac{2x^{3}y}{\sqrt{xyz}}$
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