**Q.1:** State whether the following statements are true or false. Justify your answers.

- Every irrational number is a real number.
- Every point on the number line is of the form $\sqrt{\mathrm{m}}$, where m is a natural number.
- Every real number is an irrational number.

**Solution:**

(i) Every irrational number is a real number.

- True, since the collection of real numbers is made up of rational and irrational numbers.

(ii) Every point on the number line is of the form $\sqrt{\mathrm{m}}$, where m is a natural number.

- False, since positive number cannot be expressed as square roots.

(iii) Every real number is an irrational number.

- False, as real numbers include both rational and irrational numbers. Therefore, every real number cannot be an irrational number.