$\underline{\text { Folklore }}$

Find the largest natural $n$, for which $n^{200}<5^{300}$.
Let's rewrite the inequality as: $\left(n^{2}\right)^{100}<\left(5^{3}\right)^{100}$. Therefore, it is sufficient to find the greatest natural solution to the inequality $n^{2}<125$.

## Answer

$n=11$.