The largest [integer](https://artofproblemsolving.com/wiki/index.php/Integer) $n$ for which $n^{200}<5^{300}$ is
$\mathrm{(A) \ }8 \qquad \mathrm{(B) \ }9 \qquad \mathrm{(C) \ } 10 \qquad \mathrm{(D) \ }11 \qquad \mathrm{(E) \ } 12$
Since both sides are positive, we can take the $100th$ root of both sides to find the largest integer $n$ such that $n^2<5^3$. Fortunately, this is simple to evaluate: $5^3=125$, and the largest [square](https://artofproblemsolving.com/wiki/index.php/Perfect_square) less than $125$ is $11^2=121$, so the largest $n$ is $11, \boxed{\text{D}}$.