College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Review Exercises: 113

Answer

$-9m\sqrt{2m}+5m\sqrt{m}$

Work Step by Step

Using the properties of radicals, the given expression, $ \sqrt{18m^3}-3m\sqrt{32m}+5\sqrt{m^3} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{9m^2\cdot2m}-3m\sqrt{16\cdot2m}+5\sqrt{m^2\cdot m} \\\\= \sqrt{(3m)^2\cdot2m}-3m\sqrt{(4)^2\cdot2m}+5\sqrt{(m)^2\cdot m} \\\\= 3m\sqrt{2m}-3m(4)\sqrt{2m}+5(m)\sqrt{m} \\\\= 3m\sqrt{2m}-12m\sqrt{2m}+5m\sqrt{m} \\\\= -9m\sqrt{2m}+5m\sqrt{m} .\end{array}
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