Answer
$|2x+1|$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of radicals to simplify the given expression, $
\sqrt{4x^2+4x+1}
.$
$\bf{\text{Solution Details:}}$
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{4x^2+4x+1}
\\\\=
\sqrt{(2x+1)^2}
.\end{array}
Using $\sqrt[n]{x^n}=|x|$ if $n$ is even and $\sqrt[n]{x^n}=x$ if $n$ is odd, then
\begin{array}{l}\require{cancel}
\sqrt{(2x+1)^2}
\\\\=
|2x+1|
.\end{array}
