If 1537* is a perfect square, then the digit which replace * is = ?

$$\eqalign{ & {\text{Let the missing digit be x}} \cr & \,\,\,\,\,\,\,1|\overline 1 \,\,\overline {53} \,\,\overline {7{\text{x}}} \,\,(124 \cr & \,\,\,\,\,\,\,\,\,\,|\,\,1 \cr & \,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr & \,\,\,22|\,\,\,\,\,\,\,53 \cr & \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,44 \cr & \,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr & 244\,|\,\,\,\,\,\,\,\,\,\,\,\,\,97{\text{x}} \cr & \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,976 \cr & \,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr & \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{x}} \cr & \,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr & {\text{Then, x}} = 6 \cr} $$