## NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2

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### Class 9 Maths Solution Exercise 1.2 Page: 8

#### Ex 1.2 Class 9 Maths Question 1.

**1. State whether the following statements are true or false. Justify your answers.**

**(i) Every irrational number is a real number.**

(i) True

Because all rational numbers and all irrational numbers form the set of real numbers.

**(ii) Every point on the number line is of the form √m where m is a natural number.**

Solution:

**False**

**(iii) Every real number is an irrational number.**

Solution:

**False**

#### Ex 1.2 Class 9 Maths Question 2.

**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.**

Solution:

No, if we take a positive integer, say 9, then its square root is 3, which is a rational number.

For example,

√4 = 2 is rational.

√9 = 3 is rational.

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

#### Ex 1.2 Class 9 Maths Question 3.

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

Solution:

#### Ex 1.2 Class 9 Maths Question 4.

**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 OP _{1} of unit length (see Fig. 1.9). 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 Fig. 1.9 :**

**Constructing this manner, you can get the line segment P _{n-1}Pn by square root spiral 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},….,Pn,… ., and joined them to create a beautiful spiral depicting √2, √3, √4, …**

Solution:

**Step 4: Join the 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 the OC. Here, OC will be of √3**

**Step 7: Repeat the Steps to Make √4, √5, √6….**

See Also:

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Exercise 1.1

All Maths formulas for class 9

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3

## NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2 Tips

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.2 Number Systems Explores the fundamentals of irrational numbers, what they mean, how to identify them, and also how to locate them on a number line. Therefore, students are advised to know the basic facts and differences about rational and irrational numbers for better understanding.

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.2 Questions will help the students to uncover the basics of irrational numbers and thus act as a great self-learning tool.

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