**Class 9 NCERT (CBSE) Mathematics - Chapter 1, Number System**

**NCERT Mathematics Solution - Exercise 1.2**

(Page 8)

Q1: 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

**√m**, where*m*is a natural number.(iii) Every real number is an irrational number.

Answer:

(i) The collection of real numbers is made up of rational and irrational numbers. So it is a true statement.

(ii) False, because negative numbers cannot be expressed as the square root of any other number.

(iii) Real numbers include both rational and irrational numbers. Therefore, every real number cannot be an irrational number. Hence, false statement.

Q2: 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.

Answer: If numbers such as

are considered, then here, 2 and 3 are rational numbers. Thus, the square roots of all positive integers are not irrational.

Q3: Show how

can be represented on the number line.

Answer:

Mark a point ‘A’ representing 2 on number line. Now, construct AB of unit length perpendicular to OA. Taking O as center and OB as radius, draw an arc intersecting number line at the point C where C is representing

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