College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.3: 32

Answer

$5x^2\sqrt{2}$

Work Step by Step

$\frac{\sqrt{500x^{3}}}{{\sqrt{10x^{-1}}}}$ By the quotient rule for square roots $=\sqrt{\frac{500x^{3}}{10x^{-1}}}$ $=\sqrt{50x^{3-(-1)}}$ $=\sqrt{50x^{(3+1)}}$ $=\sqrt{50x^{4}}$ $=\sqrt{25\cdot 2 \cdot x^{4}}$ $=\sqrt{25} \cdot \sqrt{x^{4}} \cdot \sqrt{2}$ $=5x^{2}\sqrt{2}$
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