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

NCERT Solutions Class 9 Maths Chapter 1 Number Systems Exercise 1.2 present here are prepared by our subject experts which makes it easy for students to learn. The students use it for reference while solving the exercise problems. The second exercise in Number Systems- Exercise 1.2 discusses irrational numbers. The solutions provide detailed and stepwise explanations of each answer, to the questions given in the exercises in the NCERT textbook for class 9. The solutions are always prepared by following NCERT guidelines so that it should cover the whole syllabus accordingly. These are very helpful in scoring well in first term examinations.

### Access other exercise solutions of Class 9 Maths Chapter 1- Number Systems

Exercise 1.1 Solutions 4 Questions ( 2 long, 2 short)

Exercise 1.3 Solutions 9 Questions ( 9 long)

Exercise 1.4 Solutions 2 Questions ( 2 long)

Exercise 1.5 Solutions 5 Questions ( 4 long 1 short)

Exercise 1.6 Solutions 3 Questions ( 3 long)

### Access Answers of Maths NCERT Class 9 Chapter 1 â€“ 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.

Solution:

True

Irrational Numbers â€“ A number is said to be irrational, if it cannot be written in the p/q, where p and q are integers and q â‰  0.

i.e., Irrational numbers = â€ŽÏ€, e, âˆš3, 5+âˆš2, 6.23146â€¦. , 0.101001001000â€¦.

Real numbers â€“ The collection of both rational and irrational numbers are known as real numbers.

i.e., Real numbers = âˆš2, âˆš5, 0.102â€¦

Every irrational number is a real number, however, every real numbers are not irrational numbers.

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

Solution:

False

The statement is false since as per the rule, a negative number cannot be expressed as square roots.

E.g., âˆš9 =3 is a natural number.

But âˆš2 = 1.414 is not a natural number.

Similarly, we know that there are negative numbers on the number line but when we take the root of a negative number it becomes a complex number and not a natural number.

E.g., âˆš-7 = 7i, where i = âˆš-1

The statement that every point on the number line is of the form âˆšm, where m is a natural number is false.

(iii) Every real number is an irrational number.

Solution:

False

The statement is false, the real numbers include both irrational and rational numbers. Therefore, every real number cannot be an irrational number.

Real numbers â€“ The collection of both rational and irrational numbers are known as real numbers.

i.e., Real numbers = âˆš2, âˆš5, 0.102â€¦

Irrational Numbers â€“ A number is said to be irrational, if it cannot be written in the p/q, where p and q are integers and q â‰  0.

i.e., Irrational numbers = Ï€, e, âˆš3, 5+âˆš2, 6.23146â€¦. , 0.101001001000â€¦.

Every irrational number is a real number, however, every real number is not irrational.

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.

Â

Solution:

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

For example,

âˆš4 = 2 is rational.

âˆš9 = 3 is rational.

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

3. Show how âˆš5 can be represented on the number line.

Solution:

Step 1:Â Let line AB be of 2 unit on a number line.

Step 2:Â At B, draw a perpendicular line BC of length 1 unit.

Step 3: Join CA

Step 4:Â Now, ABC is a right angled triangle. Applying Pythagoras theorem,

AB2+BC2 = CA2

22+12 = CA2 CA2 = 5

â‡’Â CAÂ = âˆš5 . Thus, CA is a line of lengthÂ âˆš5 unit.

Step 4:Â Taking CA as a radius and A as a center draw an arc touching

the number line. The point at which number line get intersected by

arc is atÂ âˆš5 distance from 0 because it is a radius of the circle

whose center was A.

Thus,Â âˆš5Â is represented on the number line as shown in the figure.

4. Classroom activity (Constructing the â€˜square root spiralâ€™) : Take a large sheet of paper and construct the â€˜square root spiralâ€™ 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,â€¦.,Pn,â€¦ ., and joined them to create a beautiful spiral depicting âˆš2, âˆš3, âˆš4, â€¦

Solution:

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 âˆš2

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 âˆš3

Step 7: Repeat the steps to draw âˆš4, âˆš5, âˆš6â€¦.

NCERT solutions for Class 9 Maths Chapter 1 â€“ Number Systems Exercise 1.2 is the second exercise of Chapter 1 of Class 9 Maths. This exercise explains Irrational numbers.

• These NCERT Solutions help you solve and revise all questions of Exercise 1.2.
• After going through the stepwise solutions given by our subject expert teachers, you will be able to get more marks.
• It follows NCERT guidelines which help in preparing the students accordingly.
• It consists of all the important questions from the examination point of view.

#### 1 Comment

1. Prerna

Thanku for the solution of this exercise.