Squaring Numbers Ending in 5 Fast!

Ever need to quickly calculate $35^2$ or $75^2$ without a calculator? There's a super-speedy way that makes you look like a math wizard!

Subject: mental-calculation • Classes: 6–12 • Difficulty: basic

The Trick

To square any number ending in 5, say $N5$: \n1. Take the digit(s) $N$ before the '5'. \n2. Calculate $N \times (N+1)$. \n3. Append '25' to the result from step 2. \nWhy it works: A number $N5$ is $(10N+5)$. Its square is $(10N+5)^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25$. This means you calculate $N(N+1)$ and effectively multiply by 100 (by placing it before '25') then add '25'.

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