Question

If possible, let ( 5 sqrt{3} ) be a rational number.
So, ( 5 sqrt{3}=p / q ) where ( p ) and ( q ) are co-prime integers and
( q eq 0 )
So, ( sqrt{3}=frac{p}{5 q} )
So, R.H.S is a rational number and hence ( sqrt{3} ) is also rational which is a contradiction.
So our supposition is wrong. Hence, 5 is an irrational number

# Show that 5/5 is an irrational number.

Solution