# Xam Idea Class 10 Maths Chapter 1 Solutions: Real Number

Xam Idea Class 10 Maths Solutions for Chapter 1 ‘Real Numbers’ are formed according to the latest CBSE Class 10 exam guidelines. The questions provided in Xam Idea Solutions Class 10 Maths Chapter 1 covers different concepts like Euclid’s** **division lemma, Euclid’s division algorithm, fundamental theorem of arithmetic, rational and irrational numbers and applications of real numbers.

Xam Idea Class 10 Solutions Chapter 1 Real Numbers contain 6 exercises which contain 47 questions. The chapter covers questions such as very short answer type questions, short answer type questions, long answer type questions, higher-order thinking skills and value-based questions. All the questions are important from the CBSE exams perspective. All the concepts provided in the chapter will also develop a deeper understanding of further chapters in mathematics.

Instasolv offers accurate solutions to all the questions provided in Xam Idea Class 10 Maths book. The answers are designed by our subject-matter experts who have years of quality experience. All the Xam Idea solutions are easy to comprehend because the experts at Instasolv have explained every question step by step. You can access the solutions to the questions for free. Our solutions are in synchronization with guidelines provided by CBSE and NCERT for Class 10.

## Important Topics For Xam Idea Class 10 Maths Solutions Chapter 1: Real Numbers

Xam Idea Class 10 Maths Solutions are completely based on real numbers and its applications. The chapter covers topics like Euclid’s division algorithm, rational and irrational numbers, and the fundamental theorem of arithmetic. Here are a few important topics of the chapter.

**The Divisibility of Integers**: It explains to you that any positive integer can be divided by another positive integer b that leaves a remainder r which is smaller than b. The divisibility property of integers is used to compute HCF of natural numbers.

**The Fundamental Theorem of Arithmetic: **With this theorem, you can express every composite natural number as a product of primes that works on multiplication of positive integers.

**Euclid’s Division Lemma: **For the positive integers a and b, there exist whole numbers q and r that will satisfy the equation ‘a = bq + r, 0 r < b’.

**Euclid’s Division Algorithm: **You can calculate the HCF of two positive integers a and b, given the condition a > b by

Step 1: applying Euclid’s division lemma on a and b, where a=bq+r, 0r<b

Here, q and r are whole numbers.

Step 2: When r=0, HCF(a,b)=b

When r0, you can apply Euclid’s division on b and r.

b=r+rq1+r1, 0r1<b for some whole number q1 and r1.

Step 3.When r1=0, then HCF of (b,r)=r

HCF(a,b)=HCF(b,r)=HCF(a,b)=r.

You must continue the above process until the remainder is zero. The last non-zero remainder=HCF(a,b).

**Fundamental Theorem of Arithmetic:**

- This theorem states that every composite number can be factorized as the product of primes.
- The relation between HCF and LCM of two natural numbers is given by HCF X LCM= product of two natural numbers.
- The theorem also tells you that LCM of two natural numbers is always divisible by their HCF.

**Rational and Irrational Numbers:**

- A number that you can express in the form of p/q, given that p and q both are integers and q0 is called a rational number.
- An irrational number is a number that cannot be expressed in the form of p/q

### Exercise Discussion of Xam Idea Class 10 Maths Solutions Chapter 1: Real Numbers

Xam Idea Class 10 Maths Chapter 1 Real Numbers includes 6 exercises with 47 questions in total. Here is a discussion over the exercises and questions related to the chapter.

**Very Short Answer Type Questions**

This section contains a total of 12 questions that ask you to find HCF of composite numbers, decimal representation, LCM of numbers, etc. Some questions are based on Euclid’s division lemma and algorithm.

**Short Answer Type Questions – I**

You will find 9 questions in this section that cover topics like rational numbers, irrational numbers, LCM, HCF, composite numbers, etc. Some questions also ask you about general justifications.

**Short answer type Questions-II**

This section covers 11 questions that majorly ask you to find LCM of integers, HCF of integers, decimal expansion, etc. In some questions, you are also required to express a number in the form of a rational number.

**Long Answer Type Questions**

This set of exercises contains 8 questions in total. In these questions, you need to find the HCF of two numbers using Euclid’s division algorithm, LCM and HCF of integers using prime factorization method, etc. You also have to use the concept of irrational and rational numbers in some questions.

**High Order Thinking Skills **

You will find only 3 questions in this section that are designed to assess your overall understanding of the chapter. One question asks you to find the largest positive integer when different numbers are provided. Other questions are based on the topic of rational numbers.

**Value-Based Questions**

There are 4 questions in this section that assess your complete knowledge of the concepts. You have to understand the questions properly to find the values provided in the question.

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- Instasolv platform allows you to access all the Xam Idea Class 10 maths solutions that also include all the essential topics from the chapter.
- The solutions by instasolv are written according to the latest pattern of CBSE and these solutions will help you to understand the chapter in a better way.
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