Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Concept Quiz 9.4 - Page 417: 9



Work Step by Step

We use the rule $(a+b)(a-b)=a^{2}-b^{2}$ to multiply the two terms: $(2\sqrt 3+\sqrt 5)(2\sqrt 3-\sqrt 5)$ =$(2\sqrt 3)^{2}-(\sqrt 5)^{2}$ =$[2^{2}\times (\sqrt 3)^{2}]-(\sqrt 5)^{2}$ =$[4\times 3]-(5)$ =$[12]-(5)$ =$7$ Therefore, the question statement is true.
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