#### Answer

$a+1$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\sqrt{a^2+2a+1}
,$ simplifies to
\begin{array}{l}
\sqrt{(a+1)^2}
\\\\=
a+1
.\end{array}
Note that it is assumed that no radicand was formed by raising negative quantities to even powers. Thus, absolute value bars are not necessary.