Answer
$y=23$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt{y+2}+7=12
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{y+2}=12-7
\\\\
\sqrt{y+2}=5
.\end{array}
Squaring both sides of the equation above results to
\begin{array}{l}\require{cancel}
\left( \sqrt{y+2} \right)^2=(5)^2
\\\\
y+2=25
\\\\
y=25-2
\\\\
y=23
.\end{array}
Upon checking, $
y=23
$ satisfies the original equation.
