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Toggle## Class 9 Maths Chapter 1 Exercise 1.2 Solutions

**Q.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.**

**Ans: **(i) True as a real number is either rational or irrational.

(ii) False as numbers of other types (i.e., negative number) also lie on the number line.

(iii) False as rational numbers are also real numbers.

**Q.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.**

**Ans: **No, as ** $\sqrt{4}$**= 2 is a rational number.

other example, $\sqrt{9}$= 3 is a rational number.

**Q.3. Show how $\sqrt{5}$ can be represented on the number line.**

**Ans:**

**Q.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 OP _{1} of unit length. Draw a line segment P_{1}P_{2} perpendicular to OP_{1} of unit length (see Figure). Now draw a line segment P_{2}P_{3} perpendicular to OP_{2}. Then draw a line segment P_{3}P_{4} perpendicular to OP_{3}. Continuing in this manner, you can get the line segment P_{n–1}P_{n} by drawing a line segment of unit length perpendicular to OP_{n–1}. In this manner, you will have created the points P_{2}, P_{3},…., P_{n},… ., and joined them to create a beautiful spiral depicting.**