Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.7 Radicals - R.7 Exercises: 19

Answer

$\sqrt{a^{3}b^{5}}-2\sqrt{a^{7}b^{3}}+\sqrt{a^{3}b^{9}}=ab(b-2a^{2}+b^{3})\sqrt{ab}$

Work Step by Step

$\sqrt{a^{3}b^{5}}-2\sqrt{a^{7}b^{3}}+\sqrt{a^{3}b^{9}}$ Simplify each square root: $\sqrt{a^{3}b^{5}}-2\sqrt{a^{7}b^{3}}+\sqrt{a^{3}b^{9}}=...$ $...=ab^{2}\sqrt{ab}-2a^{3}b\sqrt{ab}+ab^{4}\sqrt{ab}=...$ The expressions inside square roots are all the same. Simplify by adding the coefficients: $...=(ab^{2}-2a^{3}b+ab^{4})\sqrt{ab}=...$ Take out common factor $ab$ from the expression inside parentheses: $...=ab(b-2a^{2}+b^{3})\sqrt{ab}$
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