NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2 Access Answers of Maths NCERT Class 9 Chapter 1 – Number Systems Exercise 1.2

## NCERT Solutions for Class 9 Maths Exercise 1.2

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.

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.

**Solution:**

No, the square roots of all positive integers are not irrational.

For example,

√4 = 2 is rational.

√9 = 3 is rational.

Hence, the square roots of positive integers 4 and 9 are not irrational. ( 2 and 3, respectively).

Show how √5 can be represented on the number line.

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 Fig. 1.9 :

Constructing this manner, you can get the line segment Pn-1Pn by square root spiral 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 √2, ✓3, ✓4.....

Step 1: Mark a point O on the paper. Here, O will be the center of the square root spiral.

Step 2: From O, draw a straight line, OA, of 1cm horizontally.

Step 3: From A, draw a perpendicular line, AB, of 1 cm.

Step 4: Join OB. Here, OB will be of √2

Step 5: Now, from B, draw a perpendicular line of 1 cm and mark the end point C.

Step 6: Join OC. Here, OC will be of √3

Step 7: Repeat the steps to draw √4, √5, √6….

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Exercise 1.2 is the first exercise of Chapter 1 of class 9 Maths. This exercise explains how to find rational numbers between the two given numbers.

### NCERT Solutions For Class 9 Maths Chapter 1 Number Systems Exercises

- NCERT Solutions For Class 9 Maths Chapter 1 Number Systems Exercise 1.1
- NCERT Solutions For Class 9 Maths Chapter 1 Number Systems Exercise 1.3
- NCERT Solutions For Class 9 Maths Chapter 1 Number Systems Exercise 1.4
- NCERT Solutions For Class 9 Maths Chapter 1 Number Systems Exercise 1.5
- NCERT Solutions For Class 9 Maths Chapter 1 Number Systems Exercise 1.6

**There are 8 different types of number as follows:**

- Complex Number
- Imaginary Numbe
- Real Number
- Rational number
- Irrational number
- Integers
- Whole numbers
- Natural numbers

**Decimals classifications**

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