Answer: Option A
$$\eqalign{
& \,\,\,\,\,\,\,\,2|\overline 6 \overline {40} \overline {09} \,(\,\,253 \cr
& \,\,\,\,\,\,\,\,\,\,\,|4 \cr
& \,\,\,\,\,\,\,\,\,\,\,| - - - - - \cr
& \,\,\,\,45\,|240 \cr
& \,\,\,\,\,\,\,\,\,\,\,|225 \cr
& \,\,\,\,\,\,\,\,\,\,\,| - - - - - \cr
& 503\,\,|\,\,\,\,\,\,1509 \cr
& \,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,1509 \cr
& \,\,\,\,\,\,\,\,\,\,\,| - - - - - \cr
& \,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,x \cr
& \,\,\,\,\,\,\,\,\,\,\,| - - - - - \cr
& \therefore \sqrt {64009} = 253 \cr} $$