Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

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

Alg Num Theory
Member
Registered: 2017-11-24
Posts: 665
Website

### 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)

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

Offline

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

ganesh
Registered: 2005-06-28
Posts: 27,849

### 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.

Offline