Question
If 1537* is a perfect square, then the digit which replace * is = ?
Answer: Option D
$$\eqalign{
& {\text{Let the missing digit be x}} \cr
& \,\,\,\,\,\,\,1|\overline 1 \,\,\overline {53} \,\,\overline {7{\text{x}}} \,\,(124 \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,1 \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& \,\,\,22|\,\,\,\,\,\,\,53 \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,44 \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& 244\,|\,\,\,\,\,\,\,\,\,\,\,\,\,97{\text{x}} \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,976 \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{x}} \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr
& {\text{Then, x}} = 6 \cr} $$
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$$\eqalign{
& {\text{Let the missing digit be x}} \cr
& \,\,\,\,\,\,\,1|\overline 1 \,\,\overline {53} \,\,\overline {7{\text{x}}} \,\,(124 \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,1 \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& \,\,\,22|\,\,\,\,\,\,\,53 \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,44 \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& 244\,|\,\,\,\,\,\,\,\,\,\,\,\,\,97{\text{x}} \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,976 \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{x}} \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr
& {\text{Then, x}} = 6 \cr} $$
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