Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.3 - Simplifying Radical Expressions - Exercise Set: 72

Answer

$\dfrac{\sqrt{270y^{2}}}{5\sqrt{3y^{-4}}}=\dfrac{3}{5}y^{3}\sqrt{10}$

Work Step by Step

$\dfrac{\sqrt{270y^{2}}}{5\sqrt{3y^{-4}}}$ Rewrite this expression as $\dfrac{1}{5}\sqrt{\dfrac{270y^{2}}{3y^{-4}}}$ and evaluate the division inside the square root: $\dfrac{\sqrt{270y^{2}}}{5\sqrt{3y^{-4}}}=\dfrac{1}{5}\sqrt{\dfrac{270y^{2}}{3y^{-4}}}=\dfrac{1}{5}\sqrt{90y^{2+4}}=\dfrac{1}{5}\sqrt{90y^{6}}=...$ Rewrite the expression inside the square root as $\sqrt{9\cdot10\cdot y^{6}}$ and simplify: $...=\dfrac{1}{5}\sqrt{9\cdot10\cdot y^{6}}=\dfrac{3}{5}y^{3}\sqrt{10}$
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