| Title: | Mathematics at DEC | 
| Moderator: | RUSURE::EDP | 
| Created: | Mon Feb 03 1986 | 
| Last Modified: | Fri Jun 06 1997 | 
| Last Successful Update: | Fri Jun 06 1997 | 
| Number of topics: | 2083 | 
| Total number of notes: | 14613 | 
    Hello all,
                                           -2
    	As many people know how the prove 2   is irrational.
                                                -n 
    But, is it exist a general method to prove m   is irrational/
                              -4    -7
    rational ? (for example, 3   , 4  , ...)
    
    Thanks and Rgds,
    -- Joseph
| T.R | Title | User | Personal Name | Date | Lines | 
|---|---|---|---|---|---|
| 1608.1 | An amendment ? | HGOVC::EDDIELEUNG | Eddie Leung @HGO | Mon May 11 1992 02:37 | 11 | 
|                              (1/2)     -(1/2)
    You must be thinking of 2      or 2       and in general
              (1/n)
             m        m,n being positive integers.
    
    
    Eddie.
    
    PS :  A mathematician is someone who writes A, pronounces B but thinks
          C while actually the right answer is D.
    
 | |||||
| 1608.2 | SSAG::LARY | Laughter & hope & a sock in the eye | Mon May 11 1992 03:43 | 16 | |
| Its a fairly simple extension of a proof known to the ancient Greeks to prove that if n and m are integers then n^(1/m) is either an integer or irrational; i.e. you can't have 1/m n = p/q, q>1, p and q relatively prime If you could, then you could raise both sides of that equation to the m-th power to get n = p^m / q^m or n * q^m = p^m Since p and q have no common factors, p^m must divide n; i.e. n = k*p^m, but then k * p^m * q^m = p^m, or k * q^m = 1, which means that k = q = 1 and that contradicts the premise q>1. | |||||