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#1 2017-12-03 21:18:00

Alg Num Theory
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Registered: 2017-11-24
Posts: 337
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Numbers ending in 5

To find the square of a number ending in 5:

  1. Drop the last digit 5.

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

  3. Tack on the digits 25 at the end.

For example, to find 85²:

  1. 85 “−” 5 → 8.

  2. 8 × 9 = 72.

  3. 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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#2 2017-12-03 21:41:50

ganesh
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Registered: 2005-06-28
Posts: 25,859

Re: Numbers ending in 5

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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