Note that the smallest four-digit number is 1,000. But 1,000 is not a perfect square because √1,000 = 31.6.
So, the perfect square has to be a number that should be greater than 31 and less than or equal to 32. Because, if we consider the square of 31 it would definitely have 3-digits.
So, let 32 be the number.
=> 32 = 32 × 32 = 1,024
=> 1,024 is the smallest 4-digit number which is a perfect square.