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: 4

Answer

True

Work Step by Step

We mutiply $(2-\sqrt 7)(2+\sqrt 7)$ using the rule $(a+b)(a-b)=a^{2}-b^{2}$ to see if the product is a rational number or not: $(2-\sqrt 7)(2+\sqrt 7)$ $=2^{2}-(\sqrt 7)^{2}$ $=4-7$ $=-3$ $-3$ is a part of the subset of rational numbers. Therefore, the product of $(2-\sqrt 7)(2+\sqrt 7)$ is indeed a rational number, and the statement is true.
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