Question
The least number of 4 digits which is a perfect square is = ?
Answer: Option C
Least number of 4 digits is 1000
$$\eqalign{
& \,\,\,\,3|\overline {10} \,\,\overline {00} \,\,(31 \cr
& \,\,\,\,\,\,\,|\,\,\,\,9 \cr
& \,\,\,\,\,\,\,| - - - - - - \cr
& 61|\,\,\,\,\,1\,00 \cr
& \,\,\,\,\,\,\,|\,\,\,\,\,\,61 \cr
& \,\,\,\,\,\,\,| - - - - - - \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,39 \cr
& \therefore {\left( {31} \right)^2} < 1000 < {\left( {32} \right)^2} \cr
& {\text{Hence, required number}} \cr
& = {\left( {32} \right)^2} \cr
& = 1024 \cr} $$
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Least number of 4 digits is 1000
$$\eqalign{
& \,\,\,\,3|\overline {10} \,\,\overline {00} \,\,(31 \cr
& \,\,\,\,\,\,\,|\,\,\,\,9 \cr
& \,\,\,\,\,\,\,| - - - - - - \cr
& 61|\,\,\,\,\,1\,00 \cr
& \,\,\,\,\,\,\,|\,\,\,\,\,\,61 \cr
& \,\,\,\,\,\,\,| - - - - - - \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,39 \cr
& \therefore {\left( {31} \right)^2} < 1000 < {\left( {32} \right)^2} \cr
& {\text{Hence, required number}} \cr
& = {\left( {32} \right)^2} \cr
& = 1024 \cr} $$
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