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

(i) Every irrational number is a real number.

(ii) Every point on the number line is of the form where m is a natural number

(iii) Every real number is an irrational number.

(i) True, since the real numbers are collection of rational and irrational numbers

(ii) False, since positive number cannot be expressed as square roots

(iii) False, as real numbers consist of both rational and irrational numbers. Therefore, every real number may not be an irrational number

43