Squaring a number that ends in 5, instantly

Question

Here are some squares: 15 squared = 225, 25 squared = 625, 35 squared = 1,225, 45 squared = 2,025, 65 squared = 4,225, 95 squared = 9,025.

What is the trick for squaring any number ending in 5, and why does it work? Use it to square 105 and 115 in your head.

Accepted Answer

Take the digits before the 5, multiply that number by one more than itself, and write 25 after the result. Examples. 35 squared: 3 × 4 = 12, so 1,225. 65 squared: 6 × 7 = 42, so 4,225. 95 squared: 9 × 10 = 90, so 9,025. 105 squared: 10 × 11 = 110, so 11,025. 115 squared: 11 × 12 = 132, so 13,225. Why it works. A number ending in 5 can be written as 10n + 5, where n is everything before the 5. Its square is (10n + 5) squared = 100n squared + 100n + 25 = 100 × n(n + 1) + 25. The term 100 × n(n + 1) contributes the digits n(n + 1) followed by two zeros, and the 25 fills those two places. So the …

Squaring a number that ends in 5, instantly

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