Square 1007 in your head

Question

Solve in your head. What is 1007^2? Aim: under 10 seconds.

Accepted Answer

Expand around 1000: 1007^2 = (1000 + 7)^2 = 1{,}000{,}000 + 14{,}000 + 49 = 1{,}014{,}049. The hazard is the middle term 2 \cdot 1000 \cdot 7 = 14{,}000 and lining up the zeros. The clean way to dodge it is the slide n^2 = (n-d)(n+d) + d^2 with d = 7: 1007^2 = (1000)(1014) + 49 = 1{,}014{,}000 + 49 = 1{,}014{,}049. One factor becomes 1000, so there is no middle term to misplace: write 1014, tack on the thousands, then add 49. The answer assembles itself. Takeaway. Just above a power of ten, use (n-d)(n+d) + d^2 so one factor collapses to the round number. E.g. 1004^2 = 1000 	imes 1008 + 16 =…

Square 1007 in your head

Your answer

More Mental Math questions