# RS Aggarwal Class 10 Chapter 1 Solutions (Real Numbers)

RS Aggarwal Solutions for Class 10 Maths Chapter 1 is a perfect resource to learn about real numbers. The concepts discussed in this chapter of RS Aggarwal Class 10 Maths Solutions include fundamentals of arithmetic theorems, Euclid’s division lemma and its applications, rational and irrational numbers and some important results on these numbers. Having a strong base on real numbers is important to grasp other complex topics such as polynomials and quadratic equations.

This chapter has 47 questions divided into 5 exercises. Our subject matter experts have given solutions to each of the questions in this chapter with clarity and easily comprehensible manner. Our clear explanations would help you revise all concepts of the chapter quickly. These solutions will clarify many of your doubts which you might find difficult to get clarified in the classroom.

Seeking help from solutions for RS Aggarwal Class 10 Chapter 1 provided by our academic team would help you enhance your problem-solving skills. We have solved the exercise questions in a step-by-step format. You would also learn some shortcut methods which will help you do much better time management in competitive exams.

## Important Topics for RS Aggarwal Solutions for Class 10 Chapter 1: Real numbers

This chapter has many definitions and theorems which give you a clear idea about real numbers. The fundamentals of arithmetic theorems are discussed along with defining the relationship between HCF and LCM of numbers.

**Fundamental Theorem of Arithmetic – Any integer greater than 1 is either a prime number or can be represented or factorized as a product of prime numbers, in the order of prime factors. This makes it easy to calculate their highest common factor (HCF) and the lowest common multiple (LCM). For example, 12 = 2**^{2}* 3^{1}**Euclid’s Division Lemma –**Euclid devised a new method of studying geometry and his division lemma is a proven statement that has been used in other branches of mathematics to prove other statements. It states that for any two positive integers i_{1}and i_{2}, there exists two unique integers u_{1}and u_{2}such that:

i_{1} = i_{2} * u_{1} + u_{2}

Where 0 <= u_{2} <=i_{2}

**LCM –**For 2 or more given natural numbers, the least common multiple of those numbers is called LCM of those numbers. For example, LCM of 10, 15, and 30 is 30**HCF – For 2 or more given natural numbers, the largest common factor is HCF of these numbers. For example, HCF of 2, 4, and 6 is 2.****HCF and LCM property – For any two numbers, the product of their HCF and LCM is equal to the product of the two numbers themselves. The rule applies to only two numbers, not three or more. If the numbers are n**_{1}and n_{2}and their HCF is h_{1}and LCM is l_{1}then h_{1}* l_{1}= n_{1}* n_{2}

For example, let the two numbers are 4, 6. Their LCM is 12 and their HCF is 2, so as per the HCF and LCM property, 12 * 2 = 4 * 6

**Rational numbers –**Any number which can be denoted as a quotient q and fraction f, where q and f are integers and f is a non zero integer, is a rational number.

For example, 5 is a rational number as it can be denoted as 5/1

1.5 is a rational number as it can be denoted as 3/2

√2 is not a rational number as there is no way to express is in quotient and fraction

**Irrational numbers –**A real number which cannot be expressed as a fraction is called an irrational number. For these numbers there decimal expansion does not terminate nor are they periodic. For example, π

### Exercise Discussion of RS Aggarwal Solutions for Class 9, Chapter 19: Probability

- The first exercise in this chapter of RS Aggrawal Solutions has a total of 10 questions. They test your knowledge of Euclid’s division lemma and its applications, finding HCF of a set of numbers using Euclid’s lemma.
- The second exercise has 27 questions which need you to apply your expertise in finding HCF and LCM of numbers using prime factorization, finding the simplest form of factors. In some problems, HCF and LCM are given for a set of numbers where one of the numbers is missing and you need to find the missing number. There are also a few word problems on HCF and LCM.
- The third exercise has 3 questions where one needs to use their knowledge of rational numbers and prove they are a terminating or non-terminating decimal without actual division. One of the questions needs you to express irrational numbers in their simplest form as a fraction.
- The fourth exercise has 11 questions which revolve around irrational numbers and results on them. There are some definitions asked and you need to classify given numbers into rational or irrational numbers. There are some true/false type questions also.
- The fifth exercise has 23 questions. This chapter involves all the parts discussed in this chapter; fundamentals theorem of arithmetic, Euclid’s lemma, HCF, LCM, the property of HCF and LCM, rational and irrational numbers.

### Benefits of RS Aggarwal Solutions for Class 10 Chapter 1: Real numbers by Instasolv

- The solutions provided by our team of experts follow the guidelines given by CBSE. Hence it is the optimal way to learn and apply the concepts in exams.
- These RS Aggarwal Solutions are free of cost and made available to you by experts who have in-depth knowledge of this subject.
- Some topics of real numbers like irrational numbers and expressing real numbers in the simplest form could be a little difficult concept to understand, but our solutions would give you better insights.