Square 135 in your head

Question

Solve in your head. What is 135^2? Aim: under 5 seconds.

Accepted Answer

For any number ending in 5, written 10n + 5, (10n+5)^2 = 100\,n(n+1) + 25. Here n = 13, so multiply 13 	imes 14 = 182 and append 25: 135^2 = 18225. The only real work is the small product n(n+1); the trailing 25 is automatic. Takeaway. Every number ending in 5 squares to "n(n+1) then 25": 85^2 	o 8 	imes 9 = 72 	o 7225; 165^2 	o 16 	imes 17 = 272 	o 27225. One easy multiplication is the whole trick.

Square 135 in your head

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