Square 99 in your head

Question

Solve in your head, no written work. What is 99^2? Aim: under 5 seconds.

Accepted Answer

Anchor to 100: 99 = 100 - 1, so 99^2 = (100-1)^2 = 10000 - 200 + 1 = 9801. Alternative route via difference of squares: 99^2 = (99-1)(99+1) + 1 = 98 	imes 100 + 1 = 9801. Same answer, and the second route (n^2 = (n-d)(n+d) + d^2) is often even faster because it avoids the middle term. Takeaway. To square anything near a round number r, use (r \pm d)^2 = r^2 \pm 2rd + d^2, or slide to the round number with n^2 = (n-d)(n+d) + d^2. E.g. 103^2 = 106 	imes 100 + 9 = 10609.

Square 99 in your head

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