Square 48 in your head

Question

Solve in your head. What is 48^2? Aim: under 10 seconds.

Accepted Answer

Expand around 50, subtracting because 48 is below the base: 48^2 = (50 - 2)^2 = 2500 - 2\cdot 50 \cdot 2 + 4 = 2500 - 200 + 4 = 2304. Say it as a running total: "twenty-five hundred… twenty-three hundred… twenty-three-oh-four." The slide method is just as fast: n^2 = (n - d)(n + d) + d^2 with d = 2, so 48^2 = 46 	imes 50 + 4 = 2300 + 4 = 2304. Multiplying by 50 is trivial (halve, then multiply by 100): 46 	imes 50 = 2300. Takeaway. Below a round base, (b - d)^2 subtracts the middle term instead of adding it, everything else is identical to squaring above the base. When the slide lands you o…

Square 48 in your head

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