find the least number which must be added 506900 to make it a perfect square
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You add -506,899 to 506,900 to get 1. Nothing in the question says that the number to be added has to be positive, and all negative numbers are smaller than any positive numbers. If you restrict your attention to positive numbers, sqrt (506,900) = 711.691, so 712^2 is the closest square above 506,900.
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