Answer
See below.
Work Step by Step
An example when they are not equal is when $a=-4$, because $\sqrt{(-4)^2}=\sqrt{16}=4\ne-4$. We know that the square root of something must be non-negative and this is why $\sqrt{a^2}=|a|$.
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding - Page 80: 123
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