Show that 5 - 73 is irrational.

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Therefore, ( 5-frac{a}{b}=sqrt{3} ) Rearranging this equation, we get ( sqrt{3}=5-frac{a}{b}=frac{5 b-a}{b} ) since a and ( b ) are integers, we get ( 5-frac{a}{b} ) is rational, and so ( sqrt{3} ) is rational. But this contradicts the fact that ( sqrt{3} ) is irrational. This contradiction has arisen because of our incorrect assumption that ( 5-sqrt{3} ) is rational. So, we conclude that ( 5-sqrt{3} ) is irrational.

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