Squaring Numbers Ending in 5 - The Easy Way!

Ever stared at $35^2$ or $75^2$ and wished there was a super-fast way to calculate it in your head? Your wish is granted!

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

The Trick

To square any number ending in 5, like $N5$, follow these two 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 the next consecutive integer, $(N+1)$. 3. Simply append "25" to the result from step 2. *Why it works:* Any number ending in 5 can be written as $(10N + 5)$. When squared, $(10N + 5)^2 = (10N)^2 + 2(10N)(5) + 5^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25$. This shows that the first part of the answer is $N(N+1)$ multiplied by 100 (which means $N(N+1)$ followed by two zeros), and then 25 is added to it.

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