Question
The smallest number to be added to 680621 to make the sum a perfect square is = ?
Answer: Option A
$$\eqalign{
& \,\,\,\,\,\,\,\,8|\overline {68} \,\,\overline {06} \,\,\overline {21} \,(824 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,|\,\,64 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& \,\,\,162|\,\,\,\,4\,06 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,3\,24 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& 1644|\,\,\,\,\,\,\,\,\,\,82\,21 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,65\,76 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,16\,45 \cr
& \therefore {\text{Number to be added}} \cr
& = {\left( {825} \right)^2} - 680621 \cr
& = 680625 - 680621 \cr
& = 4 \cr} $$
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$$\eqalign{
& \,\,\,\,\,\,\,\,8|\overline {68} \,\,\overline {06} \,\,\overline {21} \,(824 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,|\,\,64 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& \,\,\,162|\,\,\,\,4\,06 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,3\,24 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& 1644|\,\,\,\,\,\,\,\,\,\,82\,21 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,65\,76 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,16\,45 \cr
& \therefore {\text{Number to be added}} \cr
& = {\left( {825} \right)^2} - 680621 \cr
& = 680625 - 680621 \cr
& = 4 \cr} $$
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More Questions on This Topic :
Question 4. $$99 \times 21 - \root 3 \of ? = 1968$$....
Question 10. $$\root 3 \of {\sqrt {0.000064} } = ?$$....
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