## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$|y+8|$
$\bf{\text{Solution Outline:}}$ 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}