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You're saying that x^2 = (50 + (x-50))^2 = 2500 + 2 * 50 * (x-50) + (x-50)^2 = 2500 + 100 * (x-50) + (x-50)^2. I'd be a little worried about the

You're saying that x^2 = (50 + (x-50))^2 = 2500 + 2 * 50 * (x-50) + (x-50)^2 = 2500 + 100 * (x-50) + (x-50)^2. I'd be a little worried about the number of double-digit squares in this method. I can't do them as easily as single-digit squares, which using the multiple of 10 closest to the number ensures. For example, I'd have to use another trick to calculate 13^2 = 100 + 2 * 10 * 3 + 9 = 169 in the middle of the calculation for 63^2 = 2500 + 100*13 + 13^2. But 63^2 = 3600 + 2 * 60 * 3 + 9 = 3969 is almost immediate.

biot 11y ago
That's why it's an abuse of the "number close to 50" trick. It really is meant for single digit differences from 50. The only reason it works for 75 is because hopefully 25^2 comes up often enough that people have it memorized. I know I memorized it long ago after seeing it a number of times: "twenty-five times twenty-five? six twenty-five" is easy for me to remember. If people don't have 25^2 memorized, the trick kind of falls down. Otherwise, you're right. You can break down the square of any number into (x+y)(x+y) = x^2 + 2xy + y^2. For 50, the "2x" term equals 100, and multiplying by 100 and adding to 2500 is dirt simple for anybody to do.
- dipakmehara05 11y ago
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