$$\sqrt {0.2} = ?$$

$$\eqalign{ & \,\,\,\,\,4|0\,.\,\overline {20} \,\,\overline {00} \,\,\overline {00} \,\,(.447 \cr & \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,16 \cr & \,\,\,\,\,\,\,\,\,| - - - - - - - - - - \cr & \,\,\,84|\,\,\,\,\,\,\,\,\,\,4\,00 \cr & \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,3\,36 \cr & \,\,\,\,\,\,\,\,\,\,| - - - - - - - - - - \cr & \,887|\,\,\,\,\,\,\,\,\,\,\,\,\,\,64\,00 \cr & \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,62\,09 \cr & \,\,\,\,\,\,\,\,\,\,| - - - - - - - - - - \cr & \therefore \sqrt {0.2} = 0.447 \cr} $$