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

[list=1]

[*]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.[/*]

[/list]

For example, to find 85²:

[list=1]

[*]85 “−” 5 → 8.[/*]

[*]8 × 9 = 72.[/*]

[*]72 “+” 25 → 7225.[/*]

[/list]

∴ 85² = 7225.

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

[list=*]

[*]135² = [13×14]25 = 18225.[/*]

[*]12345² = [1234×1235]25 = 152399025.[/*]

[/list]

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

[list=*]

[*]

[/list]

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

Me, or the ugly man, whatever (3,3,6)

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 48,338

Hi Alg Num Theory,

This is an excellent post! Keep it up!

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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