Square 996 in your head

Question

Solve in your head. What is 996^2? Aim: under 15 seconds.

Accepted Answer

Square around the round base 1000 using (a - b)^2 = a^2 - 2ab + b^2 with a = 1000, b = 4: 996^2 = (1000 - 4)^2 = 1{,}000{,}000 - 8{,}000 + 16 = 992{,}016. The middle term 2ab = 2 	imes 1000 	imes 4 = 8{,}000 is the only real work, and the last term b^2 = 16 is tiny. Subtract and you are done. A handy cross-check is the shopkeeper's trick: 996^2 = (996 + 4)(996 - 4) + 4^2 = 1000 	imes 992 + 16 = 992{,}000 + 16 = 992{,}016. Nudging one factor up and the other down to hit round numbers, then adding back the square of the nudge, gives the same result. Takeaway. To square a number near a round …

Square 996 in your head

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