How Can You Easily Square Big Numbers Without a Calculator?

[mepcotterell]

take any number, for example X and try and square it...

first let Y = X rounded up the nearest power, not multiple, of 10

[ X - (Y - X) ] * Y + (Y - X)^2 = X^2

it should work every time...

let X = 998

[ 998 - (1000 - 998) ] * 1000 + (1000 - 998)^2

[ 998 - 2 ] * 1000 + 2^2

996 * 1000 + 4

996000 + 4

996004

998^2 = 996004

you can do it for any number and it should work...

like 9999999999999999999999999999^2 is equal to 99999999999999999999999999980000000000000000000000000001

 

[HallsofIvy]

Yes, that's pretty trivial and pretty well known.

 

[Mike AkA Don]

Yea I figured that out out of boredem in math last year... Its neat but not practical.