Squaring Ends in 5! Super Shortcut

Ever wonder if there's a lightning-fast way to square numbers like $35^2$ or $105^2$ without a calculator? Get ready to amaze yourself!

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

The Trick

Want to square any number ending in 5 instantly? Here's how: 1. Take the digit(s) before the 5. Let's call it $N$. 2. Multiply $N$ by the next consecutive integer, $(N+1)$. 3. Append '25' to the result of step 2. That's your answer! Why it works: A 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 $N(N+1)$ forms the preceding digits, followed by 25.

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