Question
Sun May 01, 2011 By:

If 'a' is a non-zero rational number and 'b' an irrational number, then prove that 'a' square root 'b' is irrational.

Expert Reply
Sat April 30, 2011
let us assume on the contrary that a?b is rational. then there exist co-prime integers x and y such that,
 
this implies,       a?b=x/y
this implies,         ?b=x/ay
this implies,         ?b is rational   [therefore,a,x and y are integers then x/ay is a rational number]
this contradicts the fact that ?b is rational no.. so our assumption is not correct.
hence a?b is an irrational number. 
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