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

## NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.2 (Ex 1.2)

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.2 is an elaborative study material for students looking out for in-depth knowledge. The NCERT Maths Class 9 Chapter 1 is written as per NCERT and CBSE guidelines. Many tutors who are very well known names in the field of mathematics have contributed to NCERT solution for Class 9 Maths Chapter 1 to make the chapter easy for students. Vedantu provides students with a Free PDF download option for all the NCERT Solution of updated CBSE textbooks. Subjects like Science, Maths, Engish will become easy to study if you have access to Class 9 Science NCERT Solutions, Maths solutions, and solutions of other subjects that are available on Vedantu only.

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## NCERT Maths Class 9 Chapter 1 – Exercise 1.2

Exercise (1.2)

1. State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.

Ans: Write the irrational numbers and the real numbers in a separate manner.

• The irrational numbers are the numbers that cannot be represented in the form $\dfrac{p}{q},$ where $p$ and $q$ are integers and $q\ne 0.$

For example, $\sqrt{2},3\pi ,\text{ }.011011011...$ are all irrational numbers.

• The real number is the collection of both rational numbers and irrational numbers.

For example, $0,\,\pm \dfrac{1}{2},\,\pm \sqrt{2}\,,\pm \pi ,...$ are all real numbers.

Thus, it is concluded that every irrational number is a real number.

Hence, the given statement is true.

(ii) Every point on the number line is of the form $\sqrt{m}$, where m is a natural number.

Ans: Consider points on a number line to represent negative as well as positive numbers.

Observe that, positive numbers on the number line can be expressed as $\sqrt{1,}\sqrt{1.1,}\sqrt{1.2},\sqrt{1.3},\,...$, but any negative number on the number line cannot be expressed as $\sqrt{-1},\sqrt{-1.1},\sqrt{-1.2},\sqrt{-1.3},...$, because these are not real numbers.

Therefore, it is concluded from here that every number point on the number line is not of the form $\sqrt{m}$, where $m$ is a natural number.

Hence, the given statement is false.

(iii) Every real number is an irrational number.

Ans: Write the irrational numbers and the real numbers in a separate manner.

• The irrational numbers are the numbers that cannot be represented in the form $\dfrac{p}{q},$ where $p$ and $q$ are integers and $q\ne 0.$

For example, $\sqrt{2},3\pi ,\text{ }.011011011...$ are all irrational numbers.

• Real numbers are the collection of rational numbers (Ex: $\dfrac{1}{2},\dfrac{2}{3},\dfrac{3}{5},\dfrac{5}{7},$……) and the irrational numbers (Ex: $\sqrt{2},3\pi ,\text{ }.011011011...$).

Therefore, it can be concluded that every irrational number is a real number, but

every real number cannot be an irrational number.

Hence, the given statement is false.

2. Are the square roots of all positive integer numbers irrational? If not, provide an example of the square root of a number that is not an irrational number.

Ans: Square root of every positive integer does not give an integer.

For example: $\sqrt{2},\sqrt{3,}\sqrt{5},\sqrt{6},...$ are not integers, and hence these are irrational numbers. But $\sqrt{4}$ gives $\pm 2$ , these are integers and so, $\sqrt{4}$ is not an irrational number.

Therefore, it is concluded that the square root of every positive integer is not an irrational number.

3. Represent $\sqrt{5}$ on the number line.

Ans: Follow the procedures to get $\sqrt{5}$ on the number line.

• Firstly, Draw a line segment $AB$ of $2$ unit on the number line.

• Secondly, draw a perpendicular line segment $BC$ at $B$ of $1$ units.

• Thirdly, join the points $C$ and $A$, to form a line segment $AC$.

• Fourthly, apply the Pythagoras Theorem as

\begin{align} & A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}} \\ & A{{C}^{2}}={{2}^{2}}+{{1}^{2}} \\ & A{{C}^{2}}=4+1=5 \\ & AC=\sqrt{5} \\ \end{align}

• Finally, draw the arc $ACD$, to find the number $\sqrt{5}$ on the number line as given in the diagram below.

## NCERT Maths Class 9 Chapter 1 – Exercise 1.2

Chapter 1 Maths Class 9 is the number system. Number system forms the foundation of subsequent understanding of the subject Maths for students. This chapter deals with various kinds of number system according to your syllabus. The number system is the base on whose understanding stands the entire world of Maths. There it is necessary to understand them in detail to score well in the exam. These solutions by Vedantu are available as a free PDF download.

There are various different types of number system. The different types are as follows:

• Natural Numbers - these numbers are used for counting and always starts with one.

• Whole Numbers - this is the set of all-natural numbers including zero

• Integers - the set of all whole numbers and their respective negative numbers is called the integers.

• Rational Numbers - any number that can be written in the form of a ratio of two natural numbers is a rational number.

• Irrational Numbers - any number that cannot be written in the form of a ratio of two natural numbers is irrational.

Maths NCERT Solutions for Class 9 Chapter 1 Exercise 1.2

This particular exercise in Chapter 1 has a total of four questions to be answered. These questions tend to check the basic understanding of the chapter for the students. This question tests your understanding of all the theories and properties of the chapter of natural number.

The number system Class 9 covers all the basic concepts of number system which is eventually useful for other chapters like sets. The whole concept of real numbers. Whole numbers and the entire number system will be a part of your study journey forever. They are the foundation on which the entire branch of arithmetic math will be eventually built. Get the Class 9th Maths Chapter 1 NCERT solutions to ensure you understand all these concepts in detail.

Why Vedantu is Your Best Option?

1. Why should I opt for Vedantu’s NCERT solutions for class 9 maths Chapter 1 Exercise 1.2?

A. NCERT solutions for class 9 maths chapter 1 – Number Systems Exercise 1.2 is the second exercise of Chapter 1 of class 9 Maths. This exercise deals with Irrational numbers especially. Below are the advantages of opting for Vedantu’s NCERT Solutions.

• These NCERT Solutions help you solve and revise all the questions from exercise 1.2.in a very less time.

• After going through the stepwise solutions given by our subject expert teachers, you will be able to get more marks.

• First and foremost, these solutions will help the students score the highest possible marks.

• These are designed as per the NCERT guidelines which help in preparing the Class 9 students accordingly.

• The solutions consist of answers to all the important questions from the final examination point of view.

2. What is Class 9 maths Chapter 1 Exercise 1.2 all about?

A. NCERT Solutions Class 9 Maths Chapter 1 Number Systems Exercise 1.2 offered by Vedantu are prepared by our subject matter experts which makes it easy for the CBSE board students to learn efficiently. The students refer to these while solving the exercise problems. Exercise 1.2 or the second exercise in Number Systems deals with the irrational numbers. These provide an in-depth and stepwise explanation of each of the questions given in the exercises in the NCERT textbook for class 9 chapter 2. The solutions are prepared as per the latest NCERT curriculum and guidelines so that it should cover the whole syllabus accordingly. These are very helpful in scoring the best possible marks in the examinations.

3. How many questions are there in Class 9 maths Chapter 1 Exercise 1.2?

A. Class 9 Maths Chapter 1 Exercise 1.2 of the NCERT textbook consists of four questions in total. Among which, three are long type questions and one short question. Our Vedantu solutions consist of answers to all these questions crafted by our excellent experts.