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: 36

Answer

$6\sqrt{5}-6\sqrt{3}$

Work Step by Step

Using $a(b+c)=ab+ac$ or the Distributive Property and the properties of radicals, the given expression, $ \sqrt{3}(2\sqrt{15}-3\sqrt{4}) ,$ is equivalent to \begin{array}{l}\require{cancel} (\sqrt{3})(2\sqrt{15})-(\sqrt{3})(3\sqrt{4}) \\\\= 2\sqrt{15(3)}-3\sqrt{4(3)} \\\\= 2\sqrt{45}-3\sqrt{12} \\\\= 2\sqrt{9\cdot5}-3\sqrt{4\cdot3} \\\\= 2\sqrt{(3)^2\cdot5}-3\sqrt{(2)^2\cdot3} \\\\= 2\cdot3\sqrt{5}-3\cdot2\sqrt{3} \\\\= 6\sqrt{5}-6\sqrt{3} .\end{array}
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