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Revision Notes

Class 8

Maths

Chapter 7 Cubes And Cube Roots

Cubes and Cube Roots Class 8 Maths Chapter 6 CBSE Notes - 2025-26

Q: 8. When is it better to use the estimation method for finding cube roots over prime factorisation?

The estimation method is a fast mental shortcut best used when you are absolutely certain that the given number is a perfect cube. It relies on analysing the unit digit and the remaining part of the number. However, the prime factorisation method is more reliable and fundamental because it works for any number and also serves to verify if the number is a perfect cube in the first place. For exams, always rely on prime factorisation for accurate solutions.

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Maths Notes for Chapter 6 Cubes and Cube Roots Class 8 - FREE PDF Download

In Cbse Class 8 Maths Notes Chapter 6, you will dive into the world of cubes and cube roots. This chapter helps you understand what cubes and cube roots are, why they matter, and how to find them easily. If you ever got confused about when a number is a perfect cube or struggled with cube roots in your maths homework, these notes are here to make things clear and simple.

For a smooth study plan, don’t forget to explore the Class 8 Maths Revision Notes which break down every concept using easy examples and short tricks. You can also prepare better by checking which topics are most important in the subject so you can score well in your CBSE exam.

To prepare effectively, take a look at the Class 8 Maths Syllabus for the latest chapters and topics as per CBSE guidelines. Vedantu’s simple approach will help you revise faster and feel confident before your exams.

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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}} $

Related Study Materials for Maths Class 8 Chapter 6 Cubes and Cube Roots

S.No.	Important Study Material Links for Class 6 Maths Chapter 6
1.	Class 8 Maths Cubes and Cube Roots Important Questions
2.	Class 6 Maths Cubes and Cube Roots NCERT Solutions
3.	Class 6 Maths Cubes and Cube Roots Exemplar Solutions

Revision Notes Links For Class 8 Maths Revision Notes

S.No	Class 8 Maths Chapter Wise Revision Notes links
1	Chapter 1: Rational Numbers Notes
2	Chapter 2: Linear Equations in One Variable Notes
3	Chapter 3: Understanding Quadrilaterals Notes
4	Chapter 4: Data Handling Notes
5	Chapter 5: Squares and Square Roots
6	Chapter 7: Comparing Quantities
7	Chapter 8: Algebraic Expressions and Identities
8	Chapter 9: Mensuration Notes
9	Chapter 10: Exponents and Powers Notes
10	Chapter 11: Direct and Inverse Proportions Notes
11	Chapter 12: Factorisation Notes
12	Chapter 13: Introduction to Graphs Notes

CBSE Class 8 Maths Study Materials

S.No	Class 8 Maths Study Materials
1	CBSE Class 8 Maths NCERT Solutions
2	CBSE Class 8 Maths Important Questions
3	CBSE Class 8 Maths Formulas
4	CBSE Class 8 Maths RD Sharma Solutions
5	CBSE Class 8 Maths RS Aggarwal Solutions
6	CBSE Class 8 Maths NCERT Exemplar Solutions

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 6 Cubes and Cube Roots Notes

Class 8 Maths has an excellent syllabus that aims to develop a strong conceptual foundation among the students. Chapter 6 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 6 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 6. We at Vedantu provide Cubes and Cube Root Class 8 Notes free PDF. Along with revision notes of Class 8 Maths Chapter 6, 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 6 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.

Download Class 8 Maths Chapter 6 revision notes free PDF provided by Vedantu and see the difference in yourself. You can download them on your PC, laptops, and mobile phones as per your convenience. Now, surprising your teachers, friends, and relatives is not a big deal. You can do it by making the right decision in your life. Download Maths Class 8 Cubes and Cube Roots Notes by clicking on the PDF link given below and start revising the chapter.

Advantages of CBSE Class 8 Maths Chapter 6 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 6 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 6.

Through Class 8 Maths Chapter 6, 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 6 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 6

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 6

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 6 for clearing your chapter concepts, you should practise the exercise questions given in the NCERT textbook along with NCERT Class 8 Maths Chapter 6 solutions provided by Vedantu. Download Class 8 Revision Notes Maths Chapter 6 available on this page and score more marks in your examinations.

Key Features of Vedantu’s Class 8 Maths Chapter 6 Revision Notes

Some of the benefits of the Vedantu’s Class 8 Maths Chapter 6 revision notes are discussed below:

Easy and comprehensible revision notes.
Created by Vedantu’s subject matter experts.
Free Pdfs Downloads.
Created as per the latest CBSE syllabus.
Easy to understand the important topics.
Increases question paper solving speed.
Improvement in marks in the examination.
Helpful for quick revision.

Download CBSE Class 8 Maths Chapter 6 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 6 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 Maths Chapter 6 CBSE Notes - 2025-26

1. What key concepts should I summarise for a quick revision of Class 8 Maths Chapter 6, Cubes and Cube Roots?

For a quick revision of this chapter, you should create a summary of the following key concepts:

Cubes and Perfect Cubes: Understanding what a cube number is and how to identify a perfect cube using prime factorisation.
Properties of Cubes: Recalling patterns, such as the cube of an even number is even, and the cube of an odd number is odd.
Cube Roots: Understanding that finding a cube root is the inverse operation of finding a cube.
Methods for Finding Cube Roots: Mastering the prime factorisation method for accuracy and the estimation method as a shortcut for perfect cubes.

2. What is the core concept of a perfect cube as covered in the revision notes?

A perfect cube is a natural number that is the cube of another natural number. For a quick recap, the key test is this: when you perform the prime factorisation of a number, it is a perfect cube if every prime factor appears in a group of three. For example, in the prime factorisation of 216 = 2 × 2 × 2 × 3 × 3 × 3, both prime factors 2 and 3 appear in triplets, confirming 216 is a perfect cube.

3. What are some important properties of cube numbers that are useful for a quick summary?

Key properties of cubes to remember for a quick summary include:

The cube of an even number will always be even (e.g., 4³ = 64).
The cube of an odd number will always be odd (e.g., 5³ = 125).
Cubes of negative integers are always negative (e.g., (-2)³ = -8).
The unit digit of a number's cube is determined by the unit digit of the number itself, which is a helpful pattern for estimation.

4. How do you find the cube root of a number using the prime factorisation method?

The prime factorisation method is a fundamental technique to revise. To find a cube root using this method, follow these steps:

Resolve the given number into its prime factors.
Group the identical prime factors into triplets (sets of three).
From each triplet, take one factor.
Multiply these chosen factors together. The product is the cube root of the original number.

For example, for 1728, the factors are (2×2×2) × (2×2×2) × (3×3×3). Taking one from each group gives 2 × 2 × 3 = 12.

5. Why must a number's prime factors appear in groups of three for it to be a perfect cube?

This is a core principle of the chapter. For a number 'n' to be a perfect cube, it must be the result of an integer 'a' multiplied by itself three times (a × a × a). When 'a' is broken down into its prime factors, cubing it means you cube each of those prime factors. This process naturally results in every prime factor in the final number 'n' appearing in a group of three. For instance, if a = 10 (2×5), then its cube n = 10³ = (2×5)³ = 2³ × 5³ = (2×2×2)×(5×5×5).

6. How is finding the cube of a number different from multiplying it by 3?

This is a common point of confusion. Here’s a clear distinction for your revision:

Cubing a number means multiplying that number by itself three times. For example, the cube of 4 is 4 × 4 × 4 = 64.
Multiplying a number by 3 is a form of repeated addition. For example, 4 multiplied by 3 is 4 + 4 + 4 = 12.

Remembering that cubing involves exponential growth (a power of 3) is a key takeaway.

7. For a chapter summary, what is a key difference between the properties of perfect squares and perfect cubes?

A key difference to highlight in your summary is how they treat negative numbers:

A perfect square of a non-zero number is always positive. This is because a negative number multiplied by itself becomes positive (e.g., (-5)² = 25).
A perfect cube can be negative. This is because a negative number multiplied by itself three times remains negative (e.g., (-5)³ = -125).

8. When is it better to use the estimation method for finding cube roots over prime factorisation?

The estimation method is a fast mental shortcut best used when you are absolutely certain that the given number is a perfect cube. It relies on analysing the unit digit and the remaining part of the number. However, the prime factorisation method is more reliable and fundamental because it works for any number and also serves to verify if the number is a perfect cube in the first place. For exams, always rely on prime factorisation for accurate solutions.