NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Exercise 1.2 are provided by us to assist students in understanding the concepts and solving the exercises.
The solutions offer step-by-step explanations for each question and are designed to cover the entire syllabus as per NCERT guidelines. The second exercise in this chapter focuses on irrational numbers.
These solutions can be used as a reference while solving the exercise problems and can be beneficial in scoring well on board exams.
NCERT Solutions for Class 9 Maths Chapter-1 Number System Exercise 1.2
Class 9 maths exercise 1.2 question number 1. 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.
Sol. (i) True, real numbers are a collection of rational and irrational numbers.
(ii) False, the square root of a negative number can be a natural number.
(iii) False, For example, 2 is a real number but not an irrational number.
Class 9 maths exercise 1.2 question number 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.
Sol. No, For example, √25 = 5 is a rational number.
Class 9 maths exercise 1.2 question number 3. Show how √5 can be represented on the number line.
Sol. Step 1: Let line AB be of 2 units on a number line.
Step 2: 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 Pythagoras theorem,
⇒ AB2+BC² = CA²
⇒ 2²+1²= CA²
⇒ CA² = 5
⇒ CA = √5.
Thus, CA is a line of length √5 units.
Step 5: Taking CA as a radius and A as a center draw an arc touching the number line. The point at which the number line gets intersected by are is at √5 distance from 0 because it is a radius of the circle whose center was A.
Thus, √5 is represented on the number line as shown in the figure.
Class 9 maths exercise 1.2 question number 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 PIP2 perpendicular to OP, of unit length (see Fig. 1.9). Now draw a line segment P₂P, perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP. Continuing in Fig. 1.9:
Constructing this manner, you can get the line segment P. Pn by square root spiral drawing a line segment of unit length perpendicular to OP. In this manner, you will have created the points Ps P.Pn. and joined them to create a beautiful spiral depicting √2, 3, 4….
Sol. Do Yourself.
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