Prove that 3 root 5 -2 is an irrational number
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Assume that 3√5−2 is rational
3√5−2 = a/b where a and b are co- prime integers
3√5 = a - 2b / b
√5= a- 2b / 3b
RHS is of the form p/ q therefore, LHS is also rational. But it contradicts the fact that root 5 is irrational due to our incorrect assumption that 3√5−2 is rational. Hence, 3√5−2 is irrational
3√5−2 = a/b where a and b are co- prime integers
3√5 = a - 2b / b
√5= a- 2b / 3b
RHS is of the form p/ q therefore, LHS is also rational. But it contradicts the fact that root 5 is irrational due to our incorrect assumption that 3√5−2 is rational. Hence, 3√5−2 is irrational
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