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
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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