# RD Sharma Chapter 1 Class 10 Maths Exercise 1.5 Solutions

RD Sharma Chapter 1 Class 10 Maths Exercise 1.1 Solutions -Real Number is written by expert mathematics teachers. The solutions in the chapter are written according to RD Sharma’s latest Class 10 Mathematics Solutions course. This chapter will introduce you to real numbers. Here you will learn about Euclid’s division lemma and Euclid’s division algorithm. This chapter also introduces you to the fundamental principle of arithmetic, the fundamental factor, the method of application of LCM, HCF, and HCF and LCM in real-world problems.

RD Sharma Chapter 1 Class 10 Maths Exercise 1.5 Solutions: It consists of 12 questions, and all the questions are based on rational and irrational numbers. All the questions follow the same pattern and you have to test the questions based on the equation or positive prime numbers.

## Download RD Sharma Chapter 1 Class 10 Maths Exercise 1.5 Solutions

RD Sharma Solutions Class 10 Maths Chapter 1 Ex 1.5

## Important Definition for RD Sharma Chapter 1 Class 10 Maths Exercise 1.5 Solutions

• Euclid’s Division Lemma

This section also teaches you about Euclid’s Division Lemma. It states that the given two integers a and b, there always exists a unique pair of integers which are named as q and r such that a=b×q+r and 0≤r<b.

• Euclid’s Division Algorithm

This part of Class 10 Maths Real Numbers teaches you about Euclid’s algorithm theorem. It tells you how Euclid’s Division Algorithm is based on Euclid’s Division Lemma.

Here you will also come to know how to find the HCF of the two given numbers with Euclid’s Division Algorithm say p and g, where p>g. Now, if we are applying Euclid’s theorem to this, then p=g×q+r and 0≤r<g.

Suppose, if we consider r=0, with the HCF as g, now, if we apply Euclid’s division Lemma to g(the divisor) and r (the remainder). With this, we get another pair of remainder and quotient. This method is repeated until a remainder 1 is attained. The divisor that step is the HCF of the given set of numbers.

• The Fundamental Theorem of Arithmetic

This section of RD Sharma Solutions for Class 10 Maths Chapter 1-Real Numbers, introduces you to prime factorisation and how it is the method of representing a natural number through the multiplication of prime numbers. For example, 36=2 x 2 x3 x 3 is the prime factorisation of 36.

It also explains the Fundamental Theorem of Arithmetic which states that the prime factorisation of the given number should be unique if the arrangement of prime factors is ignored.

For Example 36= 2 x 2 x 3 x 3 or 36 = 2 x 3 x 2 x 3.

In this section, you’ll also learn the method of finding LCM, method of finding HCF, the product of two numbers which is HCF X LCM of the two numbers and application of HCF and LCM in real-world problems.

• Revisiting Irrational Numbers

This element of Class 10 Maths Real Numbers, explains about the irrational numbers. Basically, these are the numbers which cannot be expressed in the form of a fraction (p/q). Examples of Irrational numbers are √2,π, and e.

• Revisiting Rational Numbers and Their Decimal Expansions

This element of RD Sharma Solutions for Class 10 Maths Chapter 1-Real Numbers, teaches you about the terminating and non-terminating decimals.

1. When a number stops at a certain point, then it is called terminating decimal.
Example: 8.42, 7.58. 1.23, and so on.
2. When a decimal number doesn’t terminate after a certain point, then it is considered as non-terminating decimals.

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