The 'Ends in 5' Squaring Secret!

Ever struggle to quickly square numbers like $35^2$ or $75^2$ in your head? What if you could do it in seconds, without a calculator?

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

The Trick

Here’s how to instantly square any number ending in 5! **Step 1:** The last two digits of your answer will *always* be $25$. **Step 2:** Take the digit(s) *before* the 5. Let this number be $N$. **Step 3:** Multiply $N$ by the next consecutive whole number, which is $(N+1)$. **Step 4:** Place the result from Step 3 in front of the $25$ from Step 1. That's your answer! **Why it works:** Any number ending in 5 can be written as $(10N + 5)$. When you square this, you get $(10N + 5)^2 = (10N)^2 + 2(10N)(5) + 5^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25$. This shows the $N(N+1)$ part followed by $25$.

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