Answer
The solution is $r=\frac{2}{3}$.
Work Step by Step
The given equation is
$\Rightarrow \sqrt{5r}-\sqrt{8r-2}=0$
Add $\sqrt{8r-2}$ to each side.
$\Rightarrow \sqrt{5r}-\sqrt{8r-2}+\sqrt{8r-2}=0+\sqrt{8r-2}$
Simplify.
$\Rightarrow \sqrt{5r}=\sqrt{8r-2}$
Square each side of the equation.
$\Rightarrow (\sqrt{5r})^2=(\sqrt{8r-2})^2$
Simplify.
$\Rightarrow 5r=8r-2$
Add $2-5r$ to each side.
$\Rightarrow 5r+2-5r=8r-2+2-5r$
Simplify.
$\Rightarrow 2=3r$
Divide each side by $3$.
$\Rightarrow \frac{2}{3}=r$
Check $r=\frac{2}{3}$.
$\Rightarrow \sqrt{5r}-\sqrt{8r-2}=0$
$\Rightarrow \sqrt{5(\frac{2}{3})}-\sqrt{8(\frac{2}{3})-2}=0$
$\Rightarrow \sqrt{\frac{10}{3}}-\sqrt{\frac{16}{3}-2}=0$
$\Rightarrow \sqrt{\frac{10}{3}}-\sqrt{\frac{16-6}{3}}=0$
$\Rightarrow \sqrt{\frac{10}{3}}-\sqrt{\frac{10}{3}}=0$
$\Rightarrow 0=0$
True.
Hence, the solution is $r=\frac{2}{3}$.
