$$\sqrt {1.5625} = ?$$

$$\eqalign{ & \,\,\,\,\,\,1|\overline 1 .\overline {56} \overline {25} \,(\,1.25 \cr & \,\,\,\,\,\,\,\,\,|1 \cr & \,\,\,\,\,\,\,\,\,| - - - - - \cr & \,\,\,22|\,\,\,\,56 \cr & \,\,\,\,\,\,\,\,\,|\,\,\,\,44 \cr & \,\,\,\,\,\,\,\,\,| - - - - - \cr & 245|\,\,\,1225 \cr & \,\,\,\,\,\,\,\,\,|\,\,\,1225 \cr & \,\,\,\,\,\,\,\,\,| - - - - - \cr & \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,x \cr & \,\,\,\,\,\,\,\,\,| - - - - - \cr & \therefore \sqrt {1.5625} = 1.25 \cr} $$