1. 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 \(\sqrt{m}\), where m is a natural number.

(iii) Every real number is an irrational number.

2. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

3. Show how \(\sqrt5\) can be represented on the number line.

4. Classroom activity (Constructing the ‘square root spiral’) :  Take a large sheet of paper and construct the square root spiral in the following fashion. Start with a point O and draw a line segment OP₁ of unit length. Draw a line segment P₁P₂ perpendicular to OP₁ of unit length (see Fig. 1.9). Now draw a line segment P₂P₃ perpendicular to OP₂. Then draw a line segment P₃P₄ perpendicular to OP₃. Continuing in this manner, you can get the line segment P_n-1P_n by drawing a line segment of unit length     perpendicular to OP_n-1. In this manner, you will have created the points P₂, P₃,…., P_n, … ., and joined them to create a beautiful spiral depicting \(\sqrt 2\), \(\sqrt 3\), \(\sqrt 4\), …