College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.4 - Rational Exponents and Radicals - P.4 Exercises: 7

Answer

No.

Work Step by Step

RECALL: The value of $\sqrt{x}$ is always non-negative. The expression $\sqrt{4a^2}$ can be simplified as: $=\sqrt{(2^2)(a^2)} \\=2|a|$ Note that if the absolute value is not applied, the value of $2a$ will be negative when $a$ is negative. This is not allowed. Thus, there is a need to apply absolute to $a$ to make $2|a|$ nonnegative. Therefore, the expression $\sqrt{4a62}$ is NOT necessarily equal to $2a$
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