Problem: The largest integer nnn for which n200<5300n^{200} < 5^{300}n200<5300 is
Answer Choices:
A. 888
B. 999
C. 101010
D. 111111
E. 121212
Solution:
Taking one-hundredth roots, n200<5300⟺n2<53=125n^{200}<5^{300} \Longleftrightarrow n^{2}<5^{3}=125n200<5300⟺n2<53=125. The largest perfect square less than 125125125 is 121=112121=11^{2}121=112.