Answer
$|y+8|$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Factor the radicand and use the properties of radicals to simplify the given expression, $
\sqrt{y^2+16y+64}
.$
$\bf{\text{Solution Details:}}$
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{(y+8)^2}
.\end{array}
Since $\sqrt{x^2}=|x|$ for any real value $x,$ the expression above simplifies to
\begin{array}{l}\require{cancel}
\sqrt{(y+8)^2}
\\\\=
|y+8|
.\end{array}
