Square 53 using the number nearest 50

Question

Squaring near 50 has its own slick method: 2500 is 50^2, and small offsets nudge it predictably. Solve in your head. What is 53^2? Aim: under 10 seconds.

Accepted Answer

For 50 + d, the answer is 2500 + 100d + d^2, that is, "25 plus d" hundreds, then d^2: 53^2 = (25 + 3)\,	ext{hundred} + 3^2 = 2800 + 9 = 2809. So 53^2 = \mathbf{2809}. Add the offset 3 to 25 to get 28 (hundreds), then append the square of 3, i.e. 09. Slide-method check: 53^2 = 50 	imes 56 + 3^2 = 2800 + 9 = 2809. Same. Takeaway. Near 50: (50+d)^2 = (25+d)	imes 100 + d^2. Add the offset to 25, then tack on the tiny square.

Square 53 using the number nearest 50

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