Square 103 in your head

Question

Solve in your head. What is 103^2? Aim: under 10 seconds.

Accepted Answer

Expand around 100: 103^2 = (100 + 3)^2 = 10000 + 2\cdot 100 \cdot 3 + 9 = 10000 + 600 + 9 = 10609. Around 100 the terms almost read themselves: ten thousand, plus six hundred (twice the offset times a hundred), plus the offset squared. Running total: "ten thousand… ten-six hundred… ten-six-oh-nine." The slide confirms it: 103^2 = 106 	imes 100 + 9 = 10600 + 9 = 10609. The (n+d)(n-d)+d^2 form is especially painless near 100 because 106 	imes 100 needs no work. Takeaway. For numbers a hair above 100, the cross term is just "twice the offset, then a hundred," and the last term is the offset sq…

Square 103 in your head

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