Mathematics is an essential subject of the Class 10 board exam. The syllabus of Class 10 Mathematics has 15 different chapters on various. The Central Board of Secondary Education (CBSE) has included many topics of Mathematics such as Algebra, Geometry, Trigonometry, Statistics, etc. Chapter 1 of Class 10 Mathematics is all about real numbers. This chapter is a vital part of Arithmetic. The students should study and practice this chapter sincerely. There are many exercises and a practice set of this chapter. Here, we are discussing NCERT Solution for Class 10 Maths chapter 1 exercise 1.3.Â The students will be benefited by the questions of chapter 1 ex 1.3 Class 10 maths. You can also download NCERT Solutions for Class 10 Maths to help you revise the complete syllabus and score more marks in your examination. Also, NCERT Solution Class 10 Science is available for free on Vedantu.
The Mathematics syllabus of Class 10 contains some crucial part of Mathematics such as Geometry, Algebra, Arithmetic, Trigonometry, Statistics, etc. There are 15 chapters in Class 10 in Mathematics. The chapters are real numbers, polynomials, pair of linear equations in two variables, Arithmetic progressions, quadratic equations, triangles, introduction to Trigonometry, coordinate Geometry, applications of Trigonometry, constructions, circles, the area related to circles, surface areas and volumes, probability, Statistics. There are chapters from different parts of Mathematics.
Central Board of Secondary Education (CBSE) has included some vital concepts of Arithmetic in the Class 10 Mathematics syllabus. Chapter 1 of Class 10 Mathematics is one of them. This chapter contains all about real numbers. Real numbers are a strong conceptual topic of Mathematics. From this chapter, the students will get to know the definition, properties and classification of the real number. This chapter is also an essential part of the mathematical number system. In this chapter, some examples and property proof is included for the students. By solving those examples, the students can learn the real number system easily. The property proofs will be beneficial for them. The students should practise the exercises of the textbook. They will get a good topic insight from Class 10 maths ex 1.3 NCERT solutions and it will be efficient for your practice.
Class 10 maths ex 1.3 is an important practice set for the students. This exercise contains some testing problems of real numbers. By practising those problems, the students will get a clear understanding of the properties and classification of real numbers. The examples are much efficient to clear the conceptual part. The solutions of this exercise are provided by NCERT. Class 10 maths ex 1.3 NCERT solutions are available online for free. The students can download it for their convenience.
Practising exercises of individual Mathematics chapters is essential for the Class 10 board exam. The students should practise the exercises of specific chapters sincerely. If they get solutions for those exercises after solving, that will be beneficial for the students. That is why Class 10 maths ex 1.3 NCERT solutions are necessary. It increases the confidence of the students.
1. Prove that, âˆš5 is an international number.
Solution:
Suppose, âˆš5 is rational. Therefore, there are two integers a and b, where a/b=âˆš5.
Suppose, the common factor of a and b is other than 1. So, we can assume them as co-prime numbers by dividing by the common factor.
a = bâˆš5
Or,Â 5b2 = a2
Therefore, a2 is divisible by 5 as well as a is divisible by 5.
Let, a=5k, where k is an integer
Now, (5k)2=5b2
Or, b2 = 5k2
So, b2 and b both are divisible by 5.
Hence, we can say that a and b have common factor 5, which contradicts the co-prime fact.
Therefore, âˆš5 cannot be expressed in p/q form. âˆš5 is an irrational number (proved).
2. 3+2âˆš5 is irrational - prove this.
Solution:
Suppose, 3+2âˆš5 is a rational number.
That means, there are two integers called a and b such thatÂ
a/b=3+2âˆš5
Or, a/b - 3 = 2âˆš5
Or, âˆš5 = 1/2 (a/b-3)
As a and b are integers and 1/2 (a/b - 3) will also be rational. So, âˆš5 is rational.
This fact contradicts that âˆš5 is irrational.
Hence, our consumption is false and âˆš5 is an irrational number.
1. Why Practising Chapter 1 Class 10 Maths Exercise 1.3 is Important?
Ans: Class 10 board exam is the first board exam of the students. The students read and work hard to score well in their first board exam. The Mathematics syllabus of Class 10 has diversity in the chapters. The students have to read all the different chapters and topics with the same importance. The students should practise the chapters after completing the entire syllabus. There are several exercises and practise sets for each chapter of Class 10 Mathematics. Chapters 1 Class 10 maths exercise 1.3 is one of them. Chapter 1 Class 10 maths exercise 1.3 help the students to get a strong concept of this chapter and in practising.
2. How to Download Chapter 1 Ex 1.3 Class 10 Maths?
Ans: Mathematics is a practice-based subject. The more the students will practise, the more they will get strong on the topics. They should read and complete their Mathematics syllabus. After that, they should practise as much as they can. There are individual exercises and practise sets for all the chapters of Class 10 Mathematics. For chapter 1 the exercises are ex 1.1, ex 1.2 and ex 1.3 Class 10 maths. They can download all the exercises of chapter 1 from different educational websites. Chapter 1 ex 1.3 Class 10 maths pdf is available online for free. The students can download the pdf or click the direct download link and get it.
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