Question

prove that root 3 minus root 2 is not rational number

Answer 1

let us consider root 3 is rational
therefore    root 3 = A/B
                     A= root 3B
                       A sq = 3 Bsq 
therefore   3 divides A also
                   le A= 3C
                  squaring,   Asq = 9 Csq
                                  3 Bsq= 9Csq
                                      B sq = 3 Csq
     therefore 3 divides B also
this is a contradict to the fact of co prime
 so our assumption is wrong
root 3 is irrational


similarly root 2 is irrational



irrational + irrational is not equal to ratioanl
so root 3 + root 2 is irrational