Answer
$y=19$
Work Step by Step
Using the properties of equality to isolate the radical expression results to
\begin{array}{l}\require{cancel}
\sqrt{y+6}-2=3
\\\\
\sqrt{y+6}=3+2
\\\\
\sqrt{y+6}=5
.\end{array}
Squaring both sides and isolating the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{y+6}=5
\\\\
\left( \sqrt{y+6} \right)^2=(5)^2
\\\\
y+6=25
\\\\
y=25-6
\\\\
y=19
.\end{array}
Upon checking, $
y=19
$ satisfies the original equation.
