Question

(i) ( quad 7 sqrt{5}=frac{p}{q} Rightarrow sqrt{5}=frac{p}{7 q} )
( Rightarrow sqrt{5} ) is rational. It gives contradiction.
(ii) ( frac{1}{sqrt{2}}=frac{1}{sqrt{2}} times frac{sqrt{2}}{sqrt{2}}=frac{sqrt{2}}{2} )
If possible let ( frac{sqrt{2}}{2} ) be rational.

# Prove that the following are irrationals: 0 715 (ii) 5

Solution