RD Sharma Class 10 Chapter 1 (Real Numbers) Solutions


Having understood the basics of the first chapter ‘Real Numbers’ from NCERT, you shall now proceed with solving extra questions from RD Sharma Class 10 Chapter-1. Frequently asked questions from this chapter are mainly based on two theorems, namely Euclid’s division algorithm and the Fundamental theorem of arithmetic. 

Let us understand both the theorems below. Also, find the solutions for each exercise of this chapter here. 

RD Sharma Class 10 Chapter 1 (Real Numbers) Solutions

RD Sharma - MathematicsClass 10th , RD Sharma
Chapter 1 - Real Numbers
Chapter 2 - Polynomials
Chapter 3 - Pair of Linear Equations in Two Variables
Chapter 4 - Triangles
Chapter 5 - Trigonometric Ratios
Chapter 6 - Trigonometric Identities
Chapter 7 - Statistics
Chapter 8 - Quadratic Equations
Chapter 9 - Arithmetic Progressions
Chapter 10 - Circles
Chapter 11 - Constructions
Chapter 12 - Some Application of Trigonometry
Chapter 13 - Probability
Chapter 14 - Co-ordinate Geometry
Chapter 15 - Areas Related to Circles
Chapter 16 - Surface Areas and Volumes
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Class 10th RD Sharma

Important Theorems | RD Sharma Class 10 Chapter-1

1. Euclid’s Division Lemma

According to this theorem, if you have been given two positive integers ‘a’ and ‘b’ in the question, you will find that there exists unique integers ‘q’ and ‘r’. These two pairs of integers form a relationship such that

a = bq + r, 0 ≤ r < b

2. Euclid’s Division Algorithm

By using this theorem, you can obtain the HCF of two given positive integers. Check out the stepwise procedure to obtain the HCF of two positive integers ‘c’ and ‘d’. 

Step 1: First of all, use Euclid’s division lemma to represent two given integers in the form of equation c = dq + r, where 0 ≤ r < d

Step 2: If the value of the remainder is zero, you will obtain divisor (d) as the HCF. If the value of the remainder is non-zero, then you need to apply division lemma to d and r. 

Step 3: Follow the same process till the value of remainder comes out to be zero. At this stage, the divisor obtained will be the required HCF. 

3. Fundamental Theorem of Arithmetic

By applying this theorem, you can express a composite number in the form of a product of primes. 

Concepts in RD Sharma Class 10 Chapter-1

We have provided below the concepts that you need to know before each exercise of Chapter-1 of RD Sharma Class 10 Solutions. 

Exercise 1.1: Questions will be based on Euclid’s division lemma and division algorithm.  

Exercise 1.2: Fundamental theorem of arithmetic/ prime factorisation

Exercise 1.3: To prove whether a number is irrational or not

Exercise 1.4: To check whether a rational number is terminating or non-terminating