The 'Ends in 5' Squaring Secret

Ever wondered how to square numbers like $25, 45,$ or $75$ in seconds without a calculator? 🤔 Get ready for a super-speedy math trick!

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

The Trick

Want to square any number ending in 5 instantly? Here's how: 1. Ignore the '5' for a moment. Take the digit(s) *before* the 5 (let's call this $N$). 2. Multiply $N$ by the next consecutive integer, $(N+1)$. 3. Write '25' at the end of the result from step 2. That's it! Why it works: A number ending in 5 can be written as $(10N + 5)$. When you square it, you get $(10N+5)^2 = (10N)^2 + 2(10N)(5) + 5^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25$. So, the product $N(N+1)$ becomes the 'hundreds' part, followed by '25'.

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