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) This is true because the real numbers are made up of rational and irrational numbers.
(ii) This is false. Lets take an example, we have 2.5 on the number line but it cannot be expressed as square root of a natural number.
(iii) This is false because real numbers are made up of rational and irrational numbers. Therefore, every real number cannot be an irrational number. For example, is a real number but it is not irrational.