# RD Sharma Class 8 Solutions for Maths

RD Sharma Solutions for class 8 covers different types of questions with varying difficulty levels. The solutions provided by GeeksforGeeks help to practice the questions that ensure students have a good practice of all types of questions that can be framed in the examination. By referring to the solutions given below, students can learn various ways of solving questions to improve their knowledge and get better results in their examinations.

### Chapter 1: Rational Numbers

The chapter Rational numbers deal with the basic concepts of Rational Numbers and their properties of mathematical operations applied to it. In this book, there is a total of six exercises based on this chapter. Exercise 1.1 and 1.2 covers the basic concepts and properties used while the problems in Exercises 1.3 and 1.4 covers the topic like simplification of expressions involving addition and subtraction of rational numbers, multiplication of rational numbers and its properties, division of rational numbers. However, the rest two exercises 1.5 and 1.6 discussed the questions based on the representation of rational numbers on the number line and rational numbers between two rational numbers.

- Exercise 1.1
- Exercise 1.2
- Exercise 1.3 Set 1, Set 2
- Exercise 1.4
- Exercise 1.5
- Exercise 1.6
- Exercise 1.7 Set 1, Set 2
- Exercise 1.8

### Chapter 2: Powers

The chapter powers in this book cover various topics in its three exercises. Exercise 2.1 covers negative integral exponents while exercises 2.2 and 2.3 are based on the topics like decimal number system, laws of integral exponents, use of exponents to express small numbers in standard form.

- Exercise 2.1
- Exercise 2.2 Set 1, Set 2
- Exercise 2.3

### Chapter 3: Squares and Square Roots

This chapter in the present books includes large numbers of problems covering a wide variety of topics in nine exercises. The exercises 3.1, 3.2, 3.3, and 1.4 are based on the square of a number and square numbers, properties and patterns of some square numbers, some tricks to determine the squares by column method, visual method, diagonal method. Moreover, topics like square roots, square root of a perfect square by prime factorization are covered in exercises 3.5, 3.6, 3.7, and 3.8. Further, Exercises 3.9 are based on the relation between the digits of a perfect square and its square root, square roots of perfect squares by the method of long division, square roots of rational numbers in the form of fractions, square roots of rational numbers in decimal form and approximate values of square roots by using square root tables.

- Exercise 3.1 Set 1, Set 2
- Exercise 3.2 Set 1, Set 2
- Exercise 3.3 Set 1, Set 2
- Exercise 3.4 Set 1, Set 2
- Exercise 3.5
- Exercise 3.6
- Exercise 3.7 Set 1, Set 2
- Exercise 3.8
- Exercise 3.9

### Chapter 4: Cubes and Cube Roots

The chapter Cubes and Cube Roots helps to learn the cube of a number and perfect cube numbers. This chapter contains five exercises in which Exercise 4.1 and 4.2 includes problems based on the properties of cubes of numbers, the determination of a cube of a two-digit number by column method. Later, exercises 4.3, 4.4, and 4.5 discussed the problems on the cube root of negative integers, cubes of rational numbers, cube roots of rational numbers, cube root of a negative integral perfect cube, cube root of the product of integers, and finding cube roots by using cube root tables.

- Exercise 4.1 Set 1, Set 2
- Exercise 4.2
- Exercise 4.3
- Exercise 4.4 Set 1, Set 2
- Exercise 4.5

### Chapter 5: Playing with numbers

This chapter helps to the numbers in generalized form through its three exercises. Exercise 5.1 covers the topics like interchanging the digits of a number. However, 5.2 and 5.3 include questions from various tests of divisibility like divisibility by 10, 5, 2, 9, 3, 6, 11, and 4, cryptarithms.

### Chapter 6: Algebraic Expressions and Identities

This chapter in the present book contains seven exercises. Exercises 6.1, 6.2, and 6.3 are based on addition, subtraction, multiplication using monomials, binomials are performed, and division of algebraic expressions. Further, exercises 6.4, 6.5, 6.6, and 6.7 of this chapter discussed the applications of some special identities or products.

- Exercise 6.1
- Exercise 6.2
- Exercise 6.3 Set 1, Set 2
- Exercise 6.4 Set 1, Set 2
- Exercise 6.5 Set 1, Set 2
- Exercise 6.6 Set 1, Set 2
- Exercise 6.7

### Chapter 7: Factorisation

The chapter factorisation in this book briefs the expansion of polynomials. The problems in this chapter are discussed in nine exercises, Exercises 7.1, 7.2 and 7.3 covers the basic concepts of factors of monomial, common factors, and greatest common factor of monomials. Later, in Exercise 7.4 to 7.9 factorisation by grouping the terms, factorisation of binomial expressions expressible as the difference of two squares, when the given expression is expressible as a perfect square, factorisation of polynomials are discussed in the present chapter.

- Exercise 7.1
- Exercise 7.2
- Exercise 7.3
- Exercise 7.4
- Exercise 7.5 Set 1, Set 2
- Exercise 7.6
- Exercise 7.7
- Exercise 7.8 Set 1, Set 2
- Exercise 7.9

### Chapter 8: Division of Algebraic Expressions

By this chapter the study of polynomials continues in this book. There are total six exercises that covered the topics like division of a monomial by a monomial, division of polynomials in one variable, division of a polynomial by a binomial by using long division, and division of polynomials by using factorization.

### Chapter 9: Linear Equation in One Variable

This chapter basically explains the Linear Equations with the applications of some rules, that help to solve equations with variable terms on one side and numbers on the other side. There are four exercises in total that discuss the transposition method for solving linear equations in one variable, the cross-multiplication method for solving equations, and finally applications of linear equations to practical problems.

### Chapter 10: Direct and Inverse Proportions

This chapter in the present book gives a detailed explanation of concepts of direct and inverse variations. There are only two exercises in this chapter, exercises 10.1 and 10.2 which help to understand the types of variations (direct variations, inverse variations) and their applications to practical problems.

### Chapter 11: Time and Work

The chapter Time and work contain only one exercise. This exercise 11.1 comprises the problems on the basic methods such as: Suppose A can finish a work in n days. Then, work done by A in one day is 1/n. Or, suppose that work done by A in one day is 1/n. Then, the time taken by A to finish the whole work is n days. By the applications of such methods, the problems are based on pipes and cisterns.

### Chapter 12: Percentage

This chapter contains only three exercises. Each of the three exercises discussed the percentage and its application in daily life to calculate measure and part of anything that is required.

- Exercise 12.1
- Exercise 12.2 Set 1, Set 2

### Chapter 13: Profit, Loss, Discount, and Value Added TAX (VAT)

This chapter in the present book explains the concept of the computation of profit and loss when goods and services are bought or sold along with the advanced concepts like a discount, sales tax, and value-added tax (VAT). There are only three exercises in this chapter that discussed the latter mentioned concepts.

### Chapter 14: Compound Interest

This book introduces a complete chapter on the topic of Compound Interest. There are five exercises that explain every concept related to computing the compound interest when interest is compounded annually, half-yearly, and quarterly by using formulae in exercises 14.1 to 14.4. Meanwhile, the concepts related to inverse problems on compound interest, population growth-related problems, and depreciation are discussed in later exercises 14.4 and 14.5 of this chapter.

- Exercise 14.1
- Exercise 14.2 Set 1, Set 2
- Exercise 14.3 Set 1, Set 2
- Exercise 14.4 Set 1, Set 2
- Exercise 14.5

### Chapter 15: Understanding Shapes – I (Polygons)

The first part of Understanding Shapes is discussed in this chapter which is completely based on the polygons. This chapter contains only one exercise 15.1 which covers various plane surfaces that come across in one’s everyday life.

### Chapter 16: Understanding Shapes – II (Quadrilaterals)

The second part of Understanding shapes based on the quadrilaterals only. There is only one exercise that discusses the angle sum property of a quadrilateral, interior, and exterior of a quadrilateral, convex quadrilateral, interior angle sum property, exterior angle property.

### Chapter 17: Understanding Shapes – III (Special Types of Quadrilaterals)

The third part of Understanding shapes discusses some special types of quadrilateral and their properties in its three exercises. Various types of quadrilaterals such as trapezium, parallelogram, rhombus, rectangle, and square, along with their properties are discussed in exercises 17.1 to 17.3 respectively.

- Exercise 17.1 Set 1, Set 2
- Exercise 17.2 Set 1, Set 2
- Exercise 17.3

### Chapter 18: Practical Geometry (Constructions)

This chapter is simply based on the Construction of quadrilaterals. There are five exercises that include problems like when four sides and one diagonal are given when its three sides and two diagonals are given when its four sides and one angle are given when its three sides and their included angles are given when its three angles and their two included sides are provided.

### Chapter 19: Visualising Shapes

The chapter visualising shapes is all about visualisation of 3-D shapes from their plane figures. There are only two exercises in this chapter that helps to understand the representation of three-dimensional shapes on the plane of the paper. The shapes studied are polyhedron, prisms, and pyramids, Platonic solids, visualisation of 3-D shapes through nets.

### Chapter 20: Mensuration – I (Area of a Trapezium and a Polygon)

The first part of Mensuration covered the areas of trapezium along with polygons. In three exercises, it explains the methods of determining the area of a trapezium and also problems on finding areas of some polygons by using formulas.

- Exercise 20.1 Set 1, Set 2
- Exercise 20.2 Set 1, Set 2
- Exercise 20.3

### Chapter 21: Mensuration – II (Volumes and Surface Areas of a Cuboid and a Cube)

The second part of Mensuration covered the Volumes and Surface Areas of a Cuboid and a Cube. In total of four exercises, the problems related to the surface area of cubes and cuboids along with the volume of cube and cuboids with their approach in practical problems are discussed.

- Exercise 21.1 Set 1, Set 2
- Exercise 21.2 Set 1, Set 2
- Exercise 21.3 Set 1, Set 2
- Exercise 21.4 Set 1, Set 2

### Chapter 22: **Mensuration – III (Surface Area and Volume of a Right Circular Cylinder)**

The third part of Mensuration covered the Surface Area and Volume of a Right Circular Cylinder. In total of three exercises, the problems related to the surface area of the right circular cylinder along with the volume of the right circular cylinder with its approach in practical problems are discussed.

### Chapter 23: Data Handling – I (Classification and Tabulation of Data)

The first part of Data Handling is based on the Classification and Tabulation of Data. There are only two exercises, which cover the problems related to it. The two exercises 23.1 and 23.2 helps to understand the presentation of grouped and ungrouped data and the calculation of the frequency distribution for the given data.

### Chapter 24: **Data Handling – II (Graphical Representation of Data as Histogram)**

The second part of Data Handling is based on the Graphical Representation of Data as Histogram. There is only one exercise, which covers the problems related to the most common graphic representation is the histogram.

### Chapter 25: Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

The third part of Data Handling is based on the Pictorial Representation of Data as Pie Charts or Circle Graphs. There are only two exercises, which cover the problems related to the diagrammatic representation of data with the help of a pie-charts or circle graphs.

- Exercise 25.1 Set 1, Set 2
- Exercise 25.2

### Chapter 26: Data Handling – IV (Probability)

The fourth part of Data Handling is based on Probability. There is only one exercise, which covers the problems related to the probability of occurrence of an event with the help of some experiments and their outcomes.

### Chapter 27: Introduction to Graphs

The chapter introduction to graphs is all about the construction and reading of graphs. This chapter includes only two exercises that help to understand the plotting and reading of graphs and their applications.