Question
Tue April 19, 2011 By:

Prove that square root of 'n' is not a rational number if 'n' is not a perfect square.

Expert Reply
Wed April 20, 2011
If n is not a perfect square then  is irrational
Let on the contrary say it is rational .
Then
  where p and q are coprime integers.
so n =p2/q2
 
p2 =nq2
This shows p divides q
which is a contradiction.
Hence  is irrational if n is not a perfect square.
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