$30 \cdot 37$ The largest integer $n$ that satisfies $n^{200}<5^{300}$ is
(A) 8 .
(B) 9 .
(C) 10 .
(D) 11 .
(E) 12 .
(35th American High School Mathematics Examination, 1984)
[Solution] Here we need to find the maximum integer $n$ that satisfies the condition, so we only need to consider the case of positive integers.
By the properties of inequalities,
$$
n^{200}<5^{300} \Longleftrightarrow n^{2}<5^{3}=125,
$$

Therefore, the largest square number less than 125 is $121=11^{2}$. Hence, the answer is $(D)$.