Answer: Option C
$$\eqalign{
& \,\,\,\,\,3|0\,.\,\overline {12} \,\,\overline {10} \,\,\overline {00} \,\,(0.347 \cr
& \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,9 \cr
& \,\,\,\,\,\,\,\,\,| - - - - - - - - - - \cr
& \,\,\,64|\,\,\,\,\,\,\,\,\,\,3\,10 \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,2\,56 \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - - - - \cr
& \,687|\,\,\,\,\,\,\,\,\,\,\,\,\,\,54\,00 \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,48\,00 \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - - - - \cr
& \therefore \sqrt {0.121} = 0.347 \cr} $$