Square 998 in your head

Question

Solve in your head, no written work. What is 998^2? Aim: under 8 seconds.

Accepted Answer

Anchor to 1000: 998 = 1000 - 2, so 998^2 = (1000 - 2)^2 = 1{,}000{,}000 - 4000 + 4 = 996{,}004. The middle term is 2 	imes 1000 	imes 2 = 4000; subtract it from a million and add 2^2 = 4. Alternative via the slide trick: n^2 = (n - d)(n + d) + d^2 with d = 2 gives 998^2 = 996 	imes 1000 + 4 = 996{,}004. The product 996 	imes 1000 is just "996 then three zeros," then add 4. Takeaway. The bigger the round anchor, the more it saves you: (1000 - d)^2 = 1{,}000{,}000 - 2000d + d^2. E.g. 995^2 = 990 	imes 1000 + 25 = 990{,}025.

Square 998 in your head

Your answer

More Mental Math questions