If $\sqrt{13^2-12^2}=\sqrt[n]{125}$, then $n$ is equal to

Given, $\sqrt{{13}^2-{12}^2}=\sqrt[n]{125}$
We have $\sqrt{{13}^2-{12}^2}=\sqrt{169-144}$

$=\sqrt{25}$

$=5$ 

And $\sqrt[n]{125}=5^{3/n}$
When we equate those two, we get $5^1=5^{3/n}$
Therefore by comparing powers, we get $\frac{3}{n}=1$ $\Rightarrow n=3$