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: 32

Answer

$6\sqrt{3}-3$

Work Step by Step

Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $ \sqrt{3}(6-\sqrt{3}) ,$ is equivalent to \begin{array}{l}\require{cancel} 6\sqrt{3}-\sqrt{3(3)} \\\\= 6\sqrt{3}-\sqrt{9} .\end{array} Using the properties of radicals, the expression above simplifies to \begin{array}{l}\require{cancel} 6\sqrt{3}-\sqrt{(3)^2} \\\\= 6\sqrt{3}-3 .\end{array}
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