How Can I Compute High Precision Square Roots for Special Relativity Homework?

[BOAS]

Hello,

i'm having trouble evaluating my gamma factor for my special relativity homework, because I need to compute 1 minus a very small number (8.57*10^-13). My calculator treats this value as simply 1, as does Mathematica. Although I don't know much about it, and maybe there's a way to force it to consider the small number.

Are there any methods that I could do by hand?

(I am also looking for a computer method elsewhere, but I figured this might be interesting).

Thanks!

 

[SteamKing]

Evaluating such a difference will be a problem with a standard calculator. Mathematica however should be able to handle floating point calculations to such a precision that you don't get a value of 1 for the difference.

http://reference.wolfram.com/language/ref/SetPrecision.html

 

[BOAS]

Evaluating such a difference will be a problem with a standard calculator. Mathematica however should be able to handle floating point calculations to such a precision that you don't get a value of 1 for the difference.

http://reference.wolfram.com/language/ref/SetPrecision.html

Thanks, that solves the problem at hand.

 

[Vanadium 50]

(1+x)^(1/2) is approximately 1 + x/2.