Question 760461
It should be between 900 and 1600 as their square roots respectively are 30 and 40, thus the square root that makes the smallest 4-digit perfect square is between 30 and 40. I think it's near 30. By trial and error I found out that the square of 32 is the smallest 4-digit perfect square.

{{{32^2=1024}}} 

{{{31^2=961}}}