NCERT Solutions for Class 8 Mathematics Chapter 7: Cubes and Cubes Roots
Mathematics teaches us a lot of exciting concepts and theorems which can be extremely complex to comprehend. Therefore, students need to upgrade their preparation strategy and focus more on important concepts. Also, class 8 is an important stage for the students as it prepares them for upcoming opportunities. Thus, students need regular practice and a deeper understanding of the topics.
NCERT Class 8 Mathematics Chapter 7: Cubes and Cubes Roots explains the pattern of cubes. It tells that a perfect cube or cube numbers are obtained when a number is multiplied by taking it three times. . Students learn about the relations made concerning natural numbers with original numbers. In addition, this chapter helps students understand the calculation of cube and cube roots, interesting facts and patterns related to them.
Our Extramarks NCERT Solution Class 8 Mathematics Chapter 7 are available for the students on our website or app. It covers essential topics and helps in revising the chapter properly. The Extramarks expert team has solved the questions from chapter 7 of the NCERT textbook in a step-by-step manner. It helps students strengthen their concepts. There are various types of questions given in the solutions including MCQs, long-form questions, and short-form questions as well as miscellaneous questions at the end of the solutions.
Extramarks is an online learning platform for the best study materials for lakhs of students. Further, they can access other NCERT solutions, study materials, revision notes, and their doubts.
Students can also visit our Extramarks website for exam-related updates and news. Further, students can also refer to the other solutions such as NCERT solutions class 10, NCERT solutions class 11, and NCERT solutions class 12.
Key Topics Covered in NCERT Solutions for Class 8 Mathematics Chapter 7:
Our NCERT Solutions for Class 8 Mathematics Chapter 7 is available for students on our website and app. It covers all essential topics from chapter 7- Cubes and Cube Roots. This chapter covers all the chapter-end questions along with their comprehensive answers explained with proper illustrations.
The answers deal with essential topics to build the students’ foundation while dealing with complex numbers and cube roots. Step-wise explanations of answers in simple language make this chapter exciting and fun to learn.
Some of the key topics featured in NCERT Solutions for Class 8 Mathematics Chapter 7 are:
Introduction:
Students will be introduced to various types of cubes and their cube roots. There are many other interesting patterns of cubes as well.
Cubes:
The cube of a number is the result obtained from multiplying the same number thrice. Let’s say if x is a number, then x3 = (X) x (X) x (X). A natural number “n” is said to be a perfect cube if n = m3 for some natural number m.
Properties of Cube Numbers
There are a few key features of cubes explained in NCERT Solutions for Class 8 Mathematics Chapter 7
- A cube of an even natural number is even.
- A cube of an odd natural number is odd.
- A cube of a negative number is always negative.
- Sum of the first n natural numbers’ cubes is always equal to the square of their sum.
- Numbers of the cubes ending with the digits 0, 1, 2, 3, 4, and 5 always end with digits 0, 1, 8, 1, 7, and 5.
- Cubes of the numbers which ends with unit digit 2 will have a unit digit 8. Whereas cubes of numbers that end with unit digit 8 will have a unit digit 2 Cube of numbers which end with digit 3 or 7 their cube will end with 3 or 7.
| Number |
Square |
Number |
Square |
| 1 |
1 |
7 |
49 |
| 2 |
4 |
8 |
64 |
| 3 |
9 |
9 |
81 |
| 4 |
16 |
10 |
100 |
| 5 |
25 |
11 |
121 |
| 6 |
36 |
12 |
144 |
Some exciting patterns elaborated in NCERT Solutions for Class 8 Mathematics Chapter 7:
- Cubes are exponents which are raised to the power of 3. It is a mathematical expression or number expressed where the base and n are the power or exponent to which a is presented.
- Each prime factor appears three times in its cubes.
- Factors can be grouped in triples.
- Adding consecutive odd numbers will give an even answer.
Cube Root
The cube root of a number is the value that when multiplied by itself three times produces the original value. Therefore, the cube for the number x becomes x3 or x-cubed. For example, when we take the number 5, we have 5 x 5 x 5= 125. Based on the above-mentioned, 125 is called the cube of 5. On the other hand, the cube root of a number can be the reverse process. It is denoted by ∛. For example, five is called the cube root of the number 125.
The cube root is also denoted as ⅓ as the component of a number. Cube roots have many properties, and we have elaborated on them in our Extramarks, NCERT Solutions for Class 8 Mathematics Chapter 7. Therefore, students can refer to our solution to get a hold of the formation of cube roots.
Perfect Cubes
A perfect cube is an integer that can be expressed as the product of three same or equal integers. More precisely, 125 is a perfect cube because the cube root of 5 = 5 x 5 x 5 = 125. On the other hand, 121 is not a perfect cube because no number can give the product 121 if multiplied three times. A perfect cube is always a number whose cube root is an integer.
To understand the application of perfect cubes, students can refer to NCERT Solutions for Class 8 Mathematics Chapter 7.
Prime Factorization method for the cube root
Students can calculate the cube root of a number with the help of the prime factorization method. First, start with the prime factors of the given number. The prime factors are usually denoted as a, b, c, d and so on. Next, find the most significant prime factor from these prime factors.
Properties of Perfect cube root:
Here are some properties of perfect cube roots which students can refer to NCERT Solutions for Class 8 Mathematics Chapter 7:
- The cube root of an integer is always a natural number.
- If n is an integer and the 1, 2, 3 and n are natural numbers then (1 + 2 + 3 + 4)3 = n3.
- Each positive number has two cube roots, one positive and another negative or zero, i.e. 1, 2, 3 and 4 and 5.
- The cube roots of natural numbers are divided in half equally. For example, the cube root of 8 is 2 (2 x 8 = 16). Note: The cube root of a natural number does not necessarily equal the corresponding positive rational number.
- Equivalent to the method, we can find the cube root of a natural number by multiplying any power at least twice to it, which can be expressed as follows: This method is known as the Algebraic factorization method.
NCERT Solutions for Class 8 Mathematics Chapter 7: Exercise & Solutions
NCERT Solutions for Class 8 Mathematics Chapter 7 are available for the students on our website. Along with this, students can refer to exercises and answer solutions for better performance in the exam. The solution covers all essential concepts and topics, such as cubes, and the smallest multiple is a perfect cube. Our subject matter experts prepare the exercise and solutions.
Class 8 Mathematics chapter 7 talks contain two exercises that deal with Cubes and Cube roots. The key topics covered in this chapter include cube roots through the prime factorization method and some interesting patterns. In addition, the chapter helps students understand the different numbers and the relationship between cubes and square roots.
Click the links below for specific exercise questions and solutions.
Along with this, students can also refer to other solutions for primary and secondary classes:
NCERT Exemplar for Class 8 Mathematics:
Mathematics can be challenging to handle as it involves various concepts and theories. To understand the concepts and formulas, students need to solve differential equations of different difficulty levels.
Further, it helps to boost confidence and build a solid foundation for the upcoming exams. Extramarks’ NCERT Solutions is a solved key to textual questions. By referring to this, a student can accomplish any desired learning goal like – studying a concept/chapter from scratch, revising before examination and interpreting/drawing/labeling of diagrams. As NCERT Solutions by Extramarks is available for every chapter of every subject, students can understand all the topics in an enhanced manner and ace their preparation. By accessing other NCERT study material like important questions from the chapter, frequently asked questions, MCQs, past years’ papers, and expert tips & tricks to grasp answers on the Extramarks app or website, students can leverage higher marks in their examination.
Through regular practice, students will be able to increase their understanding of the chapter and build a strong foundation on the concepts.
Key Features of NCERT Solutions for Class 8 Mathematics Chapter 7:
Below are the key features of our NCERT Solutions for Class 8 Mathematics Chapter 7:
- It covers all the chapter-end questions along with their comprehensive answers explained with solved examples.
- Through these, students will get to learn about the properties and applications of cube roots.
- The solution will help students gain confidence in the chapter and build a strong foundation.
- We have divided the solutions into small parts so that students can grasp them quickly.
- These solutions are designed as per the current CBSE syllabus, and hence, they are considered reliable sources of learning.
- Our expert team tests and checks all the solutions to ensure that they are error-free.