Answer
$y=6$
Work Step by Step
The given equation is
$\Rightarrow 5\sqrt {y-2}=10$
Divide each side by $5$.
$\Rightarrow \frac{5\sqrt {y-2}}{5}=\frac{10}{5}$
Simplify.
$\Rightarrow \sqrt {y-2}=2$
Square each side of the equation.
$\Rightarrow (\sqrt{y-2})^2=2^2$
Simplify.
$\Rightarrow y-2=4$
Add $2$ fo each side.
$\Rightarrow y-2+2=4+2$
Simplify.
$\Rightarrow y=6$
Check $y=6$.
$\Rightarrow 5\sqrt {y-2}=10$
$\Rightarrow 5\sqrt {6-2}=10$
$\Rightarrow 5\sqrt {4}=10$
$\Rightarrow 5\sqrt {2^2}=10$
$\Rightarrow 5(2)=10$
$\Rightarrow 10=10$
True.
Hence, the solution is $y=6$.
