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Alg Num Theory

Member

Registered: 2017-11-24

Posts: 693

Website

Numbers ending in 5

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)

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

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 50,892

Re: Numbers ending in 5

Hi Alg Num Theory,

This is an excellent post! Keep it up!

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