Square 115 in your head

Question

Solve in your head. What is 115^2? Aim: under 5 seconds.

Accepted Answer

The ending-in-5 rule works for any length: for 10n + 5, (10n+5)^2 = 100\,n(n+1) + 25. Here n = 11, so compute 11 	imes 12 = 132 and append 25: 115^2 = 13225. Takeaway. The trick scales as long as you can multiply n by n+1 quickly: 145^2 	o 14 	imes 15 = 210 	o 21025; 195^2 	o 19 	imes 20 = 380 	o 38025. Numbers ending in 5 should never cost you more than one small multiplication.

Square 115 in your head

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