Answer
$n=\frac{1}{4}$
Work Step by Step
The given equation is
$\Rightarrow \sqrt{n}=\sqrt{5n-1}$
Square each side of the equation.
$\Rightarrow (\sqrt{n})^2=(\sqrt{5n-1})^2$
Simplify.
$\Rightarrow n=5n-1$
Add $1-n$ to each side.
$\Rightarrow n+1-n=5n-1+1-n$
Simplify.
$\Rightarrow 1=4n$
Divide each side by $4$.
$\Rightarrow \frac{1}{4}=\frac{4n}{4}$
Simplify.
$\Rightarrow \frac{1}{4}=n$
Check $n=\frac{1}{4}$.
$\Rightarrow \sqrt{n}=\sqrt{5n-1}$
$\Rightarrow \sqrt{\frac{1}{4}}=\sqrt{5(\frac{1}{4})-1}$
$\Rightarrow \sqrt{\frac{1}{4}}=\sqrt{\frac{5}{4}-1}$
$\Rightarrow \sqrt{\frac{1}{4}}=\sqrt{\frac{5-4}{4}}$
$\Rightarrow \sqrt{\frac{1}{4}}=\sqrt{\frac{1}{4}}$
True.
Hence, the solution is $n=\frac{1}{4}$.
