State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.

(ii) Every rational number is a real number.

(iii) Every real number need not be a rational number

(iv) √n is not irrational if n is a perfect square.

(v) √n is irrational if n is not a perfect square.

(vi) All real numbers are irrational.

(i) The statement is true.

Reason: Each and every irrational number can be plotted in the real number line and hence they are all real.

(ii) The statement is true.

Reason: Each and every rational number can be plotted in the real number line and hence they are all real.

(iii) The statement is true.

Reason: The set of rational number is a subset of real number. The set of real number is composed of both rational and irrational number.

(iv) The statement is true

Reason: Square root of a positive real number is either a rational number if it’s a perfect square or else it is an irrational number.

(v) The statement is true

Reason: Square root of a positive real number is either a rational number if it’s a perfect square or else it is an irrational number.

(vi) The statement is false.

Reason: The set of irrational number is a subset of real number. The set of real number is composed of both rational and irrational number.