Answer
$y=2$.
Work Step by Step
The given equation is
$\Rightarrow \sqrt{2y}-\sqrt{y+2}=0$
Add $\sqrt{y+2}$ to both sides.
$\Rightarrow \sqrt{2y}=\sqrt{y+2}$
Square both sides.
$\Rightarrow 2y=y+2$
Subtract $y$ from both sides.
$\Rightarrow 2y-y=2$
Simplify.
$\Rightarrow y=2$
Check $y=2$.
$\Rightarrow \sqrt{2(2)}-\sqrt{2+2}=0$
$\Rightarrow \sqrt{4}-\sqrt{4}=0$
$\Rightarrow 0=0$ True.
