Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 550: 68


$-\frac{5a\sqrt { 6ab}}{b^3}$.

Work Step by Step

The given expression is $=-\sqrt {\frac{150a^3}{b^5}}$ Use the quotient rule and rewrite as the quotient of radicals. $=-\frac{\sqrt {150a^3}}{\sqrt {b^5}}$ Factor each term as a perfect square. $=-\frac{\sqrt {5^2\cdot 6a^2a}}{\sqrt {b^4b}}$ Simplify. $=-\frac{5a\sqrt { 6a}}{b^2\sqrt {b}}$ Multiply the numerator and denominator by $\sqrt b$ to remove the radical in the denominator. $=-\frac{5a\sqrt { 6a}}{b^2\sqrt {b}}\cdot \frac{\sqrt b}{\sqrt b}$ Multiply. $=-\frac{5a\sqrt { 6ab}}{b^2\sqrt {b^2}}$ Simplify. $=-\frac{5a\sqrt { 6ab}}{b^3}$.
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