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.
Number Systems
Exercise 1.2
Class 9
Number Systems
Exercise 1.2
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.
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 Pn-1Pn by drawing a line segment of unit length perpendicular to OPn-1. In this manner, you will have created the points P2, P3,…., Pn, … ., and joined them to create a beautiful spiral depicting (sqrt 2), (sqrt 3), (sqrt 4), …
