State in each case, whether true or false :

(i) The sum of two rationals is a rational.

(ii) The sum of two irrationals is an irrational.

(iii) The product of two rationals is a rational.

(iv) The product of two irrationals is an irrational.

(v) The sum of a rational and an irrational is an irrational.

(vi) The product of a rational and an irrational is a rational.

What are irrational numbers? Give ten examples.