Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set: 19

Answer

$-7\sqrt{5}$

Work Step by Step

Simplifying each term and then combining like terms, the given expression, $ 3\sqrt{45}-8\sqrt{20} ,$ is equivalent to \begin{array}{l}\require{cancel} 3\sqrt{9\cdot5}-8\sqrt{4\cdot5} \\\\= 3\sqrt{(3)^2\cdot5}-8\sqrt{(2)^2\cdot5} \\\\= 3\cdot3\sqrt{5}-8\cdot2\sqrt{5} \\\\= 9\sqrt{5}-16\sqrt{5} \\\\= -7\sqrt{5} .\end{array}
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