Square 'em Quick: Numbers Ending in 5!

Ever found yourself stuck squaring a number like 45 or 85? What if I told you there's a trick to do it almost instantly, without a calculator?

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

The Trick

To square any number ending in 5, follow these two simple steps: 1. Ignore the '5' for a moment. Take the digit(s) *before* the 5. Let's call this number $N$. 2. Multiply $N$ by $(N+1)$. 3. Append '25' to the result of your multiplication from step 2. Why it works: Any number ending in 5 can be written as $(10N + 5)$. Squaring this gives $(10N + 5)^2 = (10N)^2 + 2(10N)(5) + 5^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25$. This shows the result is $N(N+1)$ followed by '00' plus '25', which is $N(N+1)$ followed by '25'.

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