CBSE Class 8 Maths Revision Notes Chapter 7

CBSE Class 8 Mathematics Revision Notes Chapter 7 – Cubes And Cube Roots

In these Class 8 Mathematics Chapter 7 notes, students will learn about cubes and cube roots. In addition, in these Class 8 Chapter 7 Mathematics Notes, students will get to know the significant details of the chapter that are important for their final examination. Along with Chapter 7 Mathematics Class 8 Notes, Extramarks will provide students with essential questions that can be asked to prepare them quickly. Moreover, Class 8 Mathematics Notes Chapter 7 will be a student’s last-minute revision guide, providing all the necessary information. These notes are based on the CBSE Syllabus. 

A three-dimensional solid figure with equal sides is known as a cube. A common example of a cube is the dice we use to play Ludo. Let’s say we have a cube with sides that are 1 unit long. If we calculate how many of these cubes are needed to construct a cube with sides that are 2, 3, 4, or 5 units long, we will get numbers like 8, 27, 625, etc.

It can be observed that the outcome from the above operation can also be obtained by multiplying the lengths of the sides themselves three times. For instance, 2×2×2=8, 3×3×3=27; and so forth. These are known as the perfect cubes or cube numbers, as they are created by multiplying a natural number three times.

Hardy – Ramanujan Numbers.

Numbers like  1729, 4104, and 13832  can be written as the sum of cubes of two numbers in two different ways, as given below.

1729=1728+1=12³+1³ 

1729=1000+729=10³+9³

Patterns In Cubes Of Numbers:

In this part of Class 8 Mathematics Chapter 7 Notes, we will learn about the pattern in the cubes of numbers. Perfect cubes can be created by adding consecutive odd numbers. For instance, if 1 is the first perfect cube, adding the next two odd numbers will result in 2³ (3+5=8), and doing so again will result in 3³ (7+9+11=27) and so on.

When we factorise the cube of a number, the prime factors we obtained when factorising the original number will appear three times. As an illustration, the factors of 6 are 2, 3, and those of 6³ or 216 are 2×2×2×3×3×3=2³×3³.

Cube Roots

In this part of Class 8 Mathematics Chapter 7 Notes, we will learn about the cube roots. If we are given that the cube number of a is b, then we can conclude that the cube root of b is a. It is written as a=b 13=3b in mathematics, where the symbol 3 stands for cube-root.

In most cases, the prime factorisation method is used to identify cube roots. For instance, there are two steps that can be used to calculate the cube root of the number 8000;

(i) Prime factorisation of the given number

8000=2×2×2×2×2×2×5×5×5=2³×2³×5³

(ii) Applying cube root;

38000=225=20

The number is not a perfect cube if, after prime factorisation, we are unable to group the factors into a pair of three. If it is already known that the given number is a perfect cube, we can use the steps below to determine its cube root:

a) Let’s take the perfect cube, 857375, and determine its cube root. Starting with the rightmost digit, form groups of three digits. 375 will be the first group, and 857 will be the second group.

b) The first group provides the cube root’s unit digit. We get 5 at our unit’s place because, in this case, the first group of 375 ends with 5, which is only possible if the cube root’s unit place also has 5.

c) We will now determine where the second group lies in relation to the two perfect cubes. Take the smaller number since 729>857>1000; its cube root will be at the tenth position, or 9.

So, 95 will be the cube root of 857375.

Properties of cubes

  • Even and odd numbers have likewise even and odd cubes.
  • The first natural number’s cube is equal to the square of those numbers’ sums.
  • Numbers that end in 0, 1, 2, 3, 5, 6, 7, 8, and 9 form cubes that, respectively, end in 0, 1, 8, 7, 5, 6, 3, 2, and 9.

Revision Notes for CBSE Class 8 Mathematics Chapter 7 – Free PDF Download

Mathematics Class 8 Cubes And Cube Roots Notes – Free PDF Downloads

Mathematics Class 8 Cubes And Cube Roots Notes – Free PDF Downloads

About Class 8 Chapter 7 Cubes And Cube Root

These Class 7 Chapter 8 Notes will help students find the cubes and cube roots of a number. Using the estimation method and prime factorisation, students will learn how to calculate the cube root of a number. In this chapter, they will also learn how to calculate the cube of a given number. Class 8 Mathematics Chapter 7 covers topics like an introduction to cubes and cube roots, cube roots of numbers, cubes, some intriguing patterns, etc.

Students will learn how to deal with large numbers and challenging mathematical operations through Class 8 Mathematics Chapter 7 Notes. As students solve more questions, they will feel more confident in operations like division and multiplication. Class 8 Chapter 7 notes will help you understand the concepts in detail.

List  Of The Topics And Subtopics Covered In Class 8 Mathematics Chapter 7

  1. Introduction
  2. Cubes
  3. Cube Root
  4. Cube Root Through Prime factorisation Method
  5. Cube Root of a cube number

List Of The Exercise Covered In Class 8 Mathematics Chapter 7

Exercise 7.1 (3 Questions)

Questions about the perfect cube are given in this exercise. 

The following questions are asked to students:

  • Smallest multiple or factor that can be applied to the given number to produce a perfect cube.
  • Find the numbers that form the ideal cube.
  • Number of cuboids required to build a cube.

Exercise 7.2

In this exercise, students are asked to use the prime factorisation method to determine the cube root of a given number.

You should practise the exercise questions from the NCERT textbook and use Extramark’s NCERT Class 8 Mathematics Chapter 7 solutions in addition to the Class 8 Revision Notes Mathematics Chapter 7 to clarify your chapter concepts. These notes contain all the topics in the NCERT Books concisely. Download the Class 8 Revision Notes for Mathematical Chapter 7 on this page to improve your exam results. Once you go through these notes, you can easily solve CBSE Sample Papers to test your understanding. These notes also contain CBSE Extra Questions that will help students test their understanding.

Some advantages of Extramark’s Class 8 Mathematics Chapter 7 revision notes are

  • Comprehensible and easy revision notes.
  • Created by Extramark’s subject matter experts.
  • Pdf Downloads for free.
  • Made as per the latest CBSE Syllabus.
  • Important topics are easy to understand.
  • Improves question paper-solving speed.
  • Growth in marks in the examination.
  • Helpful for quick revision.

FAQs (Frequently Asked Questions)

1. What are cube numbers?

 The numbers obtained by multiplying themselves three times are called cube numbers. For example, when 2 is multiplied by three times by itself, it gives 8. So, 8 is the cube of 2. 

  1. How to find the cube root of a number?

Ans. Using the factorisation method, the cube root of a number can be found.

2. Is 729 a perfect cube?

Yes, 729 is a perfect cube as 9 × 9 × 9 = 9³ = 729. So, we can conclude that the cube root of 729 is 9.

3. What is not a perfect cube?

 If we cannot divide the number into three equal groups of factors after performing the prime factorisation, the number is not a perfect cube. For instance, 144 is not a perfect cube since there is no number that, multiplied by itself three times, produces the result 144. In other words, a number is not a perfect cube if the cube root of the number is not an integer.

4. How can the cube root formula be written in words?

Any given number raised to the power of 1/3 is called the cube root of that number.