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# Cubes and Cube Roots Class 8 Notes CBSE Maths Chapter 7 (Free PDF Download)

Last updated date: 05th Aug 2024
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## Revision Notes for CBSE Class 8 Maths Chapter 7 - Free PDF Download

CBSE Class 8 Maths Chapter 7 Cubes and Cube Roots is an essential part of this syllabus that students need to focus on. This chapter explains what a cube and cube root is and how to identify them by using the various methods explained. To make it easier, download and study the revision notes designed by the subject experts of Vedantu and find out the easier explanation to grab. Check how the experts have explained these concepts and escalate your preparation level.

If you are looking for the best revision notes for Class 8 maths Chapter 7, then Vedantu’s cubes and cube roots Class 8 notes are prime quick. These revision notes will help you to understand the concepts in a better way. These revision notes will not only help you to prepare for your school examination but also it will help you to prepare for other competitive exams like the Olympiad. CBSE Class 7 students are advised to refer and understand Cubes and Cube Root Class 8 Notes provided by Vedantu as it covers the entire chapter in a short and precise way. It also includes a set of examples that will build a strong foundation of the important concepts.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Science Students who are looking for NCERT Solutions for Class 8 Science will also find the Solutions curated by our Master Teachers really Helpful.

Also, check CBSE Class 8 Maths revision notes for All chapters:

## Maths Class 8 Cubes and Cube Roots Notes - Free PDF Downloads

Cubes:

Cube in general terms is a  $3-$ dimensional solid figure with all its sides equal. Dice, we use to play ludo is a very common example of a cube. Suppose, we have a cube with a side length of $1$  unit, and if we find the number of such cubes required to build another cube of side lengths  $2,3,4$  or  $5$  units, then we will get the numbers as  $8,27,625$, etc.

It can be noticed that the numbers we obtained above can also be found out by multiplying the length of lengths of sides thrice to itself. For example,  $2\times 2\times 2=8$ ,  $3\times 3\times 3=27$  and so on. These are called the perfect cubes or the cube numbers as they are obtained by multiplying a natural number thrice.

Hardy – Ramanujan Numbers:

Numbers such as  $1729,4104$  and  $13832$  can be written as sum of cubes of two numbers in two different ways as can be seen below:

$1729=1728+1={{12}^{3}}+{{1}^{3}}$

$1729=1000+729={{10}^{3}}+{{9}^{3}}$

Patterns In Cubes Of Numbers:

• Adding consecutive odd numbers yields perfect cubes. For example,  $1$  is the first perfect cube, then adding the next two odd numbers will give  ${{2}^{3}}(3+5=8)$  and again adding the next three consecutive odd numbers will yield  ${{3}^{3}}(7+9+11=27)$  and so on.

• The prime factors obtained when we factorize a number will appear thrice when we factorize the cube of the same number. For example, the factors of  $6$  are  $2\times 3$ , while the factors of  ${{6}^{3}}$  or  $216$  is  $2\times 2\times 2\times 3\times 3\times 3={{2}^{3}}\times {{3}^{3}}$ .

Cube Roots:

If we are given that  $b$  is the cube of a number  $a$ , then we can say that  $a$  is the cube root of  $b$ . Mathematically, it is represented as  $a={{b}^{\frac{1}{3}}}=\sqrt[3]{b}$ , where the symbol  $\sqrt[3]{{}}$  denotes cube-root.

Cube roots are generally determined by the prime factorisation method. For example, cube root of the number  $8000$  can be determined in following two steps;

i) Prime factorisation the given number;

$8000=2\times 2\times 2\times 2\times 2\times 2\times 5\times 5\times 5={{2}^{3}}\times {{2}^{3}}\times {{5}^{3}}$

ii) Applying cube root;

$\sqrt[3]{8000}=2\times 2\times 5=20$

If after prime factorisation, we fail to group the factors in a bunch of three, then the given number is not a perfect cube. If, we already know that a number is a perfect cube, then we can find its cube root in following steps:

iii) Let's take the number $857375$ which is a perfect cube and find its cube root. Start by making groups of three digits from the rightmost digit. So, the first group will be  $375$  and the second group will be  $857$.

iv) First group gives us the unit’s digit of the cube root. Like here, the first group  $375$  ends with  $5$  which is possible only when the unit place of the cube root also has  $5$, so we get  $5$  at our unit’s place.

v) Now, we will find out that between which two perfect cubes, the second group lies. Here, we have  $729 > 857 > 1000$, so take the smaller number and its cube root will be at the ten’s place, which is  $9$.

So, the cube root of $857375$ is  $95$ .

Properties Of Cubes:

• Cubes of even and odd numbers are even and odd respectively.

• The square of the sum of the first  $n$  natural numbers is equal to the sum of their cubes.

• Cubes of numbers ending with  $0,1,2,3,4,5,6,7,8$  and  $9$  end with  $0,1,8,7,4,5,6,3,2$  and  $9$  respectively.

## Importance of CBSE Class 8 Maths Chapter 7 Cubes and Cube Roots Notes

Class 8 Maths has an excellent syllabus that aims to develop a strong conceptual foundation among the students. Chapter 7 of this syllabus explains what cube and cube roots are to the students. In this chapter, students will learn to calculate cubes and cube roots of different numbers. They will also come to know the various theorems and mathematical principles related to cubes and cube roots.

To make this chapter easier to prepare, students refer to the notes compiled by the experts. These notes are ideal to follow and study the concepts. The easier version of the arithmetic principles and concepts will enable students to focus and learn them well. In fact, they will also be able to recall them faster during an exam.

Hence, the CBSE Class 8 Maths Chapter 7 Cubes and Cube Roots Notes is a part and parcel of the study material of this chapter that every student must follow.

## Maths Class 8 Cubes and Cube Roots Notes - Free PDF Downloads

These revision notes are specially formulated by experts to provide students with authentic information for the entire chapter 7. We at Vedantu provide Cubes and Cube Root Class 8 Notes free PDF.  Along with revision notes of Class 8 Maths Chapter 7, it is also suggested to refer to sample paper and previous year question paper provided by Vedantu as it helps you in solving the question speedily and accurately.

Maths Class 8 Cubes and Cube Roots Notes will help you to learn the important concepts of the chapter easily and effectively. These Class 8 Maths Chapter 7 revision notes are a better way to revise important points and formulas in no time before your examinations. You can score more marks by referring to revision notes prepared by expert teachers at Vedantu.

## Advantages of CBSE Class 8 Maths Chapter 7 Cubes and Cube Roots Notes

• The notes have been composed in a simpler format to make them easier to understand. Students will be able to grab the concepts faster and remember them accurately to formulate the right answers to all the questions asked.

• You can also refer to the notes for revising the entire chapter. You will not have to hover over the entire chapter when you have these concise notes with you to complete revising before an exam.

• Resolve doubts related to these concepts of numbers, their cubes and cube roots, without any hassle by using these notes. Take a step ahead and prepare this chapter excellently before an exam.

## About Class 8 Chapter 7 Cubes and Cube Root

Class 7 Chapter 8 Cube and Cube root help students to learn how to find the cubes and cube root of a number. Students will learn to find the cube root of a number through the prime factorization method and estimation method. They will also learn how to find the cube of a given number in this chapter. Introduction to cubes and cube root, cube root of a number, cubes, some interesting patterns, etc are some of the topics covered in Class 8 Maths Chapter 7.

Through Class 8 Maths Chapter 7, students will get to know how to deal with large numbers and difficult Mathematical operations. By solving more and more numerical questions given in the chapter, students will excel in multiplication and division on the advanced level. Revision Notes Class 8 Maths Chapter 7 will help students to clear the concepts thoroughly.

Get 100% accurate Class 8 revision notes Maths ch 7 formulated by subject expert teachers at Vedantu. We provide explanations of every topic given in the chapter as per the updated CBSE guidelines and syllabus.

## List  of the Topics and Subtopics Covered in Class 8 Maths Chapter 7

• 7.1: Introduction

• 7.2: cubes

• 7.3: Cube Root

• 7.3.1: Cube Root Through Prime factorization Method

• 7.3.2: Cube Root of a cube number

## List of the Exercise Covered in Class 8 Maths Chapter 7

### Exercise 7.1 ( 4 Questions)

In this exercise, questions related to a perfect cube are given.

Students are asked to find the following questions:

• Smallest number by which the given number must be multiplied or divided to obtain a perfect cube.

• Find the numbers which are perfect cubes.

• The total number of cuboids Prakshit needs to form a cube.

### Exercise 7.2 ( 3 Questions)

In this exercise, students are asked to find the cube root of a given number by the prime factorization method.

Other than referring to Class 8 Revision Notes Maths Ch 7 for clearing your chapter concepts, you should practise the exercise questions given in the NCERT textbook along with NCERT Class 8 Maths Chapter 7 solutions provided by Vedantu. Download Class 8 Revision Notes Maths Chapter 7 available on this page and score more marks in your examinations.

## Key Features of Vedantu’s Class 8 Maths Chapter 7 Revision Notes

Some of the benefits of the Vedantu’s Class 8 Maths Chapter 7 revision notes are discussed below:

• Easy and comprehensible revision notes.

• Created by Vedantu’s subject matter experts.

• Created as per the latest CBSE syllabus.

• Easy to understand the important topics.

• Increases question paper solving speed.

• Improvement in marks in the examination.

## Download CBSE Class 8 Maths Chapter 7 Cubes and Cube Roots Notes Free PDF

Get the free PDF version of these notes to complete your study material for this chapter. Check how the experts have designed the notes in an organised manner and use it to your advantage. Complete revising all the topics of this chapter and focus on developing your knowledge. Refer to the notes and imbibe the formulas faster to score more in the exam.

## Conclusion

Vedantu's provision of free PDF downloads for "Cubes and Cube Roots" Class 8 Notes for CBSE Maths Chapter 7 is an invaluable resource for students. These notes simplify the complex concepts of cubes and cube roots, offering a clear and structured understanding of the topic. Vedantu's commitment to providing these resources for free ensures equitable access to quality educational materials, benefiting students regardless of their background or location. These notes not only enhance mathematical comprehension but also empower students to excel in their CBSE Math exams, fostering academic success. Vedantu's dedication to education remains commendable, providing an essential aid to students' learning journey.

## FAQs on Cubes and Cube Roots Class 8 Notes CBSE Maths Chapter 7 (Free PDF Download)

1. What are cube numbers according to Revision Notes of Chapter 7 of Class 8 Maths?

The numbers which are obtained by multiplying themselves three times are called cube numbers. For example, 2 multiplied by itself three times gives 8 hence 8 is the cube of 2. When doing prime factorization of a cube number if a prime factor repeats itself 3 times then that number is called a perfect cube. There are only ten perfect cubes among 1-1000. The concept of cube numbers is important and students should practice the questions of this chapter thoroughly.

2. What are cube roots as described in Revision Notes of Chapter 7 of Class 8 Maths?

Cube roots of a number are the numbers which when multiplied by themselves give the cube of a  number. The cube root of a number, for example, 8 is denoted by 38. Memorising cube roots of some commonly used numbers can help students in quicker calculations.

3. How do you find the cube root of a number?

The cube root of a number can be found out by the prime factorization method.

To find the cube root of a number follow these steps-

For example, if you want to find the cube root of 8000,

8000 = 2222225 55

Therefore,

38000= 225

225= 20is the cube root of 8000.

Prime factorization can be used to find the cube root when we do not know whether a number is a cube or not.

4. How many exercises are there in NCERT Chapter 7 of Class 8 Maths?

There are two exercises in the Chapter 7 of NCERT Class 8 Maths textbook:

• Exercise 7.1- four questions

• Exercise 7.1 tests the students' understanding of perfect cubes and how to find them.

• Exercise 7.2- three questions

In this exercise, students will learn how to find the cube root of a number using the prime factorization method.

They will also solve problems of finding the cube root of a number using the estimation method.

5. What are the main topics in NCERT Chapter 7 of Class 8 Maths?

The Chapter 7 of NCERT Class 8 Maths textbook teaches students the concept of cube numbers and cube roots. Students will learn what are cube numbers and when are the cube numbers called perfect cubes. They will also learn the concept of cube roots. The important topic in this chapter is the methods of finding cube roots of a number using the prime factorization method. Another method that can be used is the estimation method for the numbers that are already known to be cube numbers. The students can get the solutions and notes on Vedantu website and Vedantu Mobile app for free.