Question

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.

# Show that 5 - 73 is irrational.

Solution