Answer
no
Work Step by Step
$\sqrt{a^2+4}$ is not necessarily equal to $a+2$.
For example:
When $a=1$,
$\sqrt{a^2+4} = \sqrt{1^2+4}=\sqrt{5}$
while
$a+4 =1+4=5$
The quantities are not equal.
College Algebra 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
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 - Page 29: 8
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