How to Compute Fast Any Square

An algebraic identity extremely useful for computing squares is a well known one: a² - b² = (a - b)(a + b). For our purposes, I'll rewrite it differently:

a² = (a - b)(a + b) + b².

For example, find 112². I'll take a = 100, for 100 is a number simple to manipulate and close to 112. 100 is obtained from 112 by subtracting 12 - set b = 12. Thus we have

112² = (112 - 12)(112 + 12) + 12² = 12400 + 144 = 12544.

As another example, what is 198²? Setting a = 198, b = 2, gives

198² = (198 - 2)(198 + 2) + 2² = 200·196 + 4 = 20000 + 18000 + 1200 + 4 = 39204.


[an error occurred while processing this directive]

|Contact| |Front page| |Contents| |Algebra| |Math magic|

 

Copyright © 1996-2018 Alexander Bogomolny
[an error occurred while processing this directive]
[an error occurred while processing this directive]