Square 27 with the slide trick

Question

Small squares are worth having as reflexes, and the slide method gets you there without memorising. Solve in your head. What is 27^2? Aim: under 8 seconds.

Accepted Answer

Slide up to 30 and down to 24 using n^2 = (n-d)(n+d) + d^2 with d = 3: 27^2 = 24 	imes 30 + 3^2 = 720 + 9 = 729. So 27^2 = \mathbf{729}. The product 24 	imes 30 = 720 is trivial, and +9 finishes it. Check by expansion: (30 - 3)^2 = 900 - 180 + 9 = 729. Confirmed. Takeaway. Pick d to reach the nearest multiple of 10. Then n^2 = (	ext{round})(	ext{other}) + d^2 is a single easy product plus a small square.

Square 27 with the slide trick

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