# Prove that 3+√5 is a irrational

=>3+root 5 is in the form of p/q where p and q are integers and q is not =0

=>root5=p/q-3

=>root 5=p-3q/q

as p, q and 3 are integers p-3q/3 is a rational number.

=>root 5 is a rational number.

but we know that root 5 is an irrational number.

this is an contradiction.

this contradiction has arisen because of our wrong assumption that 3+root 5 is a rational number.

hence 3+ root 5 is an irrational number.