Question
What is the least number to be added to 7700 to make it a perfect square ?
Answer: Option E
$$\eqalign{
& \,\,\,\,\,8|\overline {77} \,\,\overline {00} \,\,(87 \cr
& \,\,\,\,\,\,\,\,\,|\,\,64 \cr
& \,\,\,\,\,\,\,\,\,| - - - - - - \cr
& 167|\,\,\,13\,00 \cr
& \,\,\,\,\,\,\,\,\,|\,\,\,11\,69 \cr
& \,\,\,\,\,\,\,\,\,| - - - - - - \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,31 \cr
& \therefore {\text{Number to be added}} \cr
& = {\left( {88} \right)^2} - 7700 \cr
& = 7744 - 7700 \cr
& = 44 \cr} $$
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$$\eqalign{
& \,\,\,\,\,8|\overline {77} \,\,\overline {00} \,\,(87 \cr
& \,\,\,\,\,\,\,\,\,|\,\,64 \cr
& \,\,\,\,\,\,\,\,\,| - - - - - - \cr
& 167|\,\,\,13\,00 \cr
& \,\,\,\,\,\,\,\,\,|\,\,\,11\,69 \cr
& \,\,\,\,\,\,\,\,\,| - - - - - - \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,31 \cr
& \therefore {\text{Number to be added}} \cr
& = {\left( {88} \right)^2} - 7700 \cr
& = 7744 - 7700 \cr
& = 44 \cr} $$
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