NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2
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.
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.
(iii) Every real number is an irrational number.
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.
No, if we take a positive integer, say 9, then its square root is 3, which is a rational number.
√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.
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 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 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….
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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.