let be x the answer
x is a square than, we can write x = n^2 where n is an anteger
x is multiple of 25 than n is a multiple of 25 so we can write x = (25*p)^2 where p an integer
then x= 625*p^2
3600 <= x <= 4900 gives 5,76 <= p^2 <= 7,84 then 2,4 <= p <= 2,8
no integer number verifies 2,4 <= p <= 2,8
so there are no integer that verifies the given conditions