The least number of 4 digits which is a perfect square is = ?

Solution(By Examveda Team)

Least number of 4 digits is 1000
$$\eqalign{ & \,\,\,\,3|\overline {10} \,\,\overline {00} \,\,(31 \cr & \,\,\,\,\,\,\,|\,\,\,\,9 \cr & \,\,\,\,\,\,\,| - - - - - - \cr & 61|\,\,\,\,\,1\,00 \cr & \,\,\,\,\,\,\,|\,\,\,\,\,\,61 \cr & \,\,\,\,\,\,\,| - - - - - - \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,39 \cr & \therefore {\left( {31} \right)^2} < 1000 < {\left( {32} \right)^2} \cr & {\text{Hence, required number}} \cr & = {\left( {32} \right)^2} \cr & = 1024 \cr} $$