Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - 6-2 Multiplying and Dividing Radical Expressions - Practice and Problem-Solving Exercises - Page 371: 39



Work Step by Step

The variables are assumed to be non-zero since they are also in the denominator. RECALL: $\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ where $a$ and $b$ are non-negative and $b\ne0.$ Use the rule above to have $\require{cancel} \sqrt{\dfrac{56x^5y^5}{7xy}} \\=\sqrt{\dfrac{\cancel{56}8\cancel{x^5}x^4\cancel{y^5}y^4}{\cancel{7xy}}} \\=\sqrt{8x^4y^4} \\=\sqrt{4x^4y^4(2)} \\=\sqrt{(2x^2y^2)^2(2)} \\=2xy\sqrt{2}.$
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