Question
The value of $$\sqrt 2 $$ up to three places of decimal is = ?
Answer: Option D
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,1|\overline 2 \,.\,\,\overline {00} \,\,\overline {00} \,\,\overline {00} \,(1.414 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,|1 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& \,\,\,\,\,\,24|\,\,1\,00 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,96 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& \,\,\,281\,|\,\,\,\,\,\,\,\,\,400 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,281 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr
& 2824\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11900 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11296 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr
& \therefore \sqrt 2 = 1.414 \cr} $$
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$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,1|\overline 2 \,.\,\,\overline {00} \,\,\overline {00} \,\,\overline {00} \,(1.414 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,|1 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& \,\,\,\,\,\,24|\,\,1\,00 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,96 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& \,\,\,281\,|\,\,\,\,\,\,\,\,\,400 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,281 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr
& 2824\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11900 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11296 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr
& \therefore \sqrt 2 = 1.414 \cr} $$
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