Square 125 instantly

Question

Solve in your head. What is 125^2? Aim: under 5 seconds.

Accepted Answer

For any number ending in 5, write it as 10n + 5, where n is everything in front of the 5. Then (10n+5)^2 = 100\,n(n+1) + 25. For 125: the front is n = 12, so 12 	imes 13 = 156, append 25: 125^2 = 15625. The only extra work versus a two-digit number is the 12 	imes 13 multiply; the "append 25" step is identical. Takeaway. The rule does not care how many digits precede the 5: treat the whole front as n, compute n(n+1), and append 25. So 135^2 = 18225 (13 	imes 14 = 182) and 205^2 = 42025 (20 	imes 21 = 420) are just as mechanical as the two-digit cases.

Square 125 instantly

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