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Mathematics Problem of the Week


Home > MPOTW > 30/03/2021

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Do this square root using pencil and paper.

346846512-346846492 Don't be put off by the telephone sized numbers and, if you do use a calculator, it's likely to be give an approximation.

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Solution

Using DOTS we can rewrite the expression thus (34684651+34684649)(34684651-34684649) then do the additions ... 69369300×2 now start factor decomposition ... 693693×100×2 continue ... 77077×9×100×2 7007×11×9×100×2 1001×7×11×9×100×2 and there we complete, perhaps, the obvious factorizations?
But checking though the divisibiliy rules we find that 1001 is a multiple of seven ... 143×49×11×9×100×2 13×49×121×9×100×2 Rooting all the perfect squares ... 7×11×3×1013×2 So ... 346846512-346846492 = 231026

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