Answer
$y=3$
Work Step by Step
The given equation is
$\Rightarrow \sqrt{y+1}=\sqrt{4y-8}$
Square each side of the equation.
$\Rightarrow (\sqrt{y+1})^2=(\sqrt{4y-8})^2$
Simplify.
$\Rightarrow y+1=4y-8$
Add $8-y$ to each side.
$\Rightarrow y+1+8-y=4y-8+8-y$
Simplify.
$\Rightarrow 9=3y$
Divide each side by $3$.
$\Rightarrow \frac{9}{3}=\frac{3y}{3}$
Simplify.
$\Rightarrow 3=y$
Check $y=3$.
$\Rightarrow \sqrt{3+1}=\sqrt{4(3)-8}$
$\Rightarrow \sqrt{4}=\sqrt{12-8}$
$\Rightarrow \sqrt{4}=\sqrt{4}$
True.
Hence, the solution is $y=3$.
