It is clear from the table that
(i) A one digit number may between 1 and 9, whose square are 1 and 81.
so the number of digits may be either 1 or 2.
(ii) Two digits numbers may be between 1 and 99 whose squares are 100 and 9801. So the number of digits may be 3 or 4.
(iii) Similarly 3 digits numbers are between 100 and 999 whose square 10000 and 998001. Therefore square of any three digit number may be in 5 or 6 digits.