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.

**Solution:**

** (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.