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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 338
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To find the square of a number ending in 5:

Drop the last digit 5.

Multiply the number without the 5 by the number that’s one greater.

Tack on the digits 25 at the end.

For example, to find 85²:

85 “−” 5 → 8.

8 × 9 = 72.

72 “+” 25 → 7225.

∴ 85² = 7225.

It works for numbers with more than two digits as well:

135² = [13×14]25 = 18225.

12345² = [1234×1235]25 = 152399025.

Why does it work? Because for any integer *n* we have

*Last edited by Alg Num Theory (2017-12-03 22:00:27)*

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 26,102

Hi Alg Num Theory,

This is an excellent post! Keep it up!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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