NCERT Solutions Class 9 Maths Chapter 1 Number System: Exercise 1.2

The topic of number systems, from Class 9 Maths, are continued in Chapter 1 Exercise 1.2 with a focus on the exponent laws for real numbers. This exercise is where students learn how to solve problems with powers and roots. Understanding and using the exponent rules is important for this chapter, but moves on into many future topics in maths.

Our NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.2 detail each question clearly, step by step. The solutions correspond directly to the latest CBSE syllabus in a simple way so that students can follow the methods with little issue. This helps in broadening the students' understanding of the number system. By regularly practicing each solution, students can improve their basic math skills and their accuracy while completing questions.

1.0Download Class 9 Maths Chapter 1 Ex 1.2 NCERT Solutions PDF

Exercise 1.2 from NCERT Solutions for Class 9 Chapter 1 Number system explains the law of exponent for real numbers. Download the free PDF of NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.2 from below:

2.0NCERT Solutions Class 9 Chapter 1- Number Systems: All Exercises 

3.0NCERT Class 9 Maths Chapter 1 Exercise 1.2 : Detailed Solutions

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, since the collection of real numbers consists of rationals and irrationals.

(ii) False, because no negative number can be the square root of any natural number. Also, numbers like √2, √3, etc., can be represented, but not all points like 1.5 or 0.7.

(iii) False, 2 is a real number but it is not an irrational number (it's a rational 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, the square roots of all positive integers are not irrational.

Example: √4 = 2, is a rational number.

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

Sol. To represent √5 on the number line:

1. Draw a number line and mark point O as 0.
2. From O, mark point A at 2 units (since 5 = 2² + 1²).
3. At A, draw a perpendicular line segment AB of 1 unit length.
4. Join OB. By Pythagoras theorem, OB = √(OA² + AB²) = √(2² + 1²) = √(4+1) = √5.
5. With O as the center and OB as the radius, draw an arc that intersects the number line at point N.
6. Point N represents √5 on the number line.

Start at 0. Go 2 units to the right (point A).

From A, go 1 unit up (point B).

The hypotenuse OB has length √5.

Then, use a compass to transfer this length to the number line, marking point N.]

4.0Key Features and Benefits Class 9 Maths Chapter 1 Number System: Exercise 1.2

• These NCERT Solutions illustrate the significant rules of exponents and real numbers referred to in the syllabus under CBSE.
• Each solution is set out step-wise to help students develop a clear understanding of the method and logic involved.
• These CBSE NCERT Solutions will help students to solve the questions accurately and are useful for school exams and different Olympiads.
• Mastering and understanding this exercise will positively build a foundation for algebra and other advanced concepts covered in higher-level classes.
• Regular practice with NCERT Solutions will gradually boost confidence and comfort in working with number-based problems, generally, especially in Olympiad-style competitive examinations.