NCERT Solutions Class 9 Maths Chapter 1 Number Systems Exercise 1.2 available here are prepared by the subject-matter experts at BYJU’S, which makes it easy for students to learn. The students can use the NCERT Class 9 Maths Solutions for reference while solving the exercise problems. The second exercise in Number Systems – Exercise 1.2 discusses irrational numbers.
The NCERT solutions provide detailed and stepwise explanations of each answer to the questions given in the exercises in the textbook for Class 9. The solutions are always prepared by following NCERT guidelines so that they should cover the whole syllabus accordingly. Moreover, the NCERT solutions are very helpful in scoring well in annual examinations.
NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems Exercise 1.2
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 to Maths NCERT Class 9 Chapter 1 – Number Systems Exercise 1.2
1. State whether the following statements are true or false. Justify your answer.
(i) Every irrational number is a real number.
Solution:
True
Irrational numbers – A number is said to be irrational if it cannot be written in the p/q, where p and q are integers and q ≠0.
i.e., Irrational numbers = ‎π, e, √3, 5+√2, 6.23146…. , 0.101001001000….
Real numbers – The collection of both rational and irrational numbers is known as real numbers.
i.e., Real numbers = √2, √5, 0.102…
Every irrational number is a real number; however, every real number is not an irrational number.
(ii) Every point on the number line is of the form √m, 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.
For example, √9 = 3 is a natural number.
But √2 = 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.
For example, √-7 = 7i, where i = √-1
The statement that every point on the number line is of the form √m, 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 – The collection of both rational and irrational numbers is known as real numbers.
i.e., Real numbers = √2, √5, 0.102…
Irrational numbers – A number is said to be irrational if it cannot be written in the p/q, where p and q are integers and q ≠0.
i.e., Irrational numbers = Ï€, e, √3, 5+√2, 6.23146…. , 0.101001001000….
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.
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 (2 and 3, respectively) are not irrational.
3. Show how √5 can be represented on the number line.
Solution:
Step 1: Let line AB be of 2 units on a number line.
Step 2:Â At B, draw a perpendicular line BC of length 1 unit.
Step 3: Join CA
Step 4: Now, ABC is a right-angled triangle. Applying the Pythagoras theorem,
AB2+BC2 = CA2
22+12 = CA2 CA2 = 5
⇒ CA = √5 . Thus, CA is a line of length √5 unit.
Step 4: Taking CA as a radius and A as a centre, draw an arc touching the number line. The point at which the number line gets intersected by an arc is at √5 distance from 0 because it is the radius of the circle whose centre was A.
Thus, √5 is represented on the number line, as shown in the figure.
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 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 can create the points P2, P3,…., Pn,… ., and join them to create a beautiful spiral depicting √2, √3, √4, …
Solution:
Step 1: Mark a point O on the paper. Here, O will be the centre of the square root spiral.
Step 2: From O, draw a straight line, OA, of 1 cm 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 second exercise of Chapter 1 of Class 9 Maths. Exercise 1.2 explains the concept of irrational numbers. These solutions cover the entire topic in detail, and the key features are as follows:
- These Class 9 Maths Chapter 1 NCERT Solutions help you solve and revise all the questions of Exercise 1.2.
- By going through the stepwise solutions given by our expert teachers, you can score good marks in the annual examination.
- It follows NCERT guidelines which help in preparing the syllabus accordingly.
- It consists of all the important questions from the examination point of view.
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