13 and 14 squared all round up to 200.
13^2=169 rounded to the nearest hundred is 200
14^2=196 rounded to the nearest hundred is 200
We can't go any lower than 13 because 12^2=144, and 144 rounds to 100. We also can't go any higher than 15 because 15^2=225, and 225 rounds down to 200, not up (Thanks Irspow).
:)