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

Asked by  | 1st May, 2011, 03:12: AM

Expert Answer:

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. 

Answered by  | 30th Apr, 2011, 10:19: PM

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