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Ekadhikena Purvena: Squaring Numbers Ending in 5

"Ekadhikena Purvena" means "by one more than the one before". It is a neat shortcut for squaring any number that ends in 5. It is not magic. It is a pattern you can prove with algebra.

1. Take the number before the 5. For 65, that is 6.
2. Multiply it by the next number: 6 × 7 = 42.
3. Write 25 at the end: 42 and 25 makes 4225. So 65 × 65 = 4225.

Why does this pattern work?

Any number ending in 5 can be written as 10n + 5, where n is the number before the 5. Squaring it gives (10n + 5)² = 100n² + 100n + 25 = 100 × n(n + 1) + 25. So the first part is n × (n + 1) and the last two digits are always 25.

Try your own number ending in 5:

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