Square It Quick! Numbers Ending in 5

Ever need to quickly square a number like 35 or 75 without a calculator? What if there was a super-fast secret trick?

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

The Trick

Want to square a number ending in 5, say $X5$? Here's how: 1. Identify 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 from step 2. That's your answer! WHY it works: A number $X5$ is $10N+5$. Squaring it gives $(10N+5)^2 = (10N)^2 + 2(10N)(5) + 5^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25$. This mathematically shows why $N(N+1)$ forms the leading digits and '25' always follows.

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