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prove that is irrational number.

                    

Asked by Topperlearning User 12th December 2013, 1:40 AM
Answered by Expert
Answer:

 Let us assume, to the contrary that is rational

                = 

or    

                 --- (1)

         Therefore 2 divides  and 2 divides p.  So we can   

         write  p = 2r for some integer r

 

   Substituting this value of p = 2r in (1)

                                   

This means 2 divides to  or 2 divides q also.  Therefore, p and q have at least 2 as a common factor.  But this contradict the fact that p and q have no common factor other than 1.

 

This contradiction arises because of our wrong assumption that  is a rational number.  So we conclude that   is irrational number.

Answered by Expert 12th December 2013, 3:40 AM
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