NCERT Solutions for Class 8 Maths Chapter 7 – Cubes and Cube Roots
The NCERT Solutions for Class 8 Maths Chapter 7 is a highly recommended material to be read with great focus before your NCERT Solutions exam. Our group of maths experts has made this material very comprehensive and easy to follow for you. With the help of NCERT solutions for chapter 7 maths, you will be able to grasp the concepts of cube numbers and perfect cubes. This chapter has only 2 exercises with a total of 7 questions. Some of the questions also have subparts so you have ample questions to practice.
Our high-quality NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots will present you much about this chapter in a fun and interesting way. The concepts given in this chapter provide you with the fundamentals of the cube – what is a perfect cube, finding cubes, and cube roots, etc. You will also learn that the numbers which can be represented in two different manners as a sum of the two cubes are known as Hardy-Ramanujam Numbers. For example: 1729, 4104, 13832 etc.
CBSE class 8 maths NCERT chapter 7 is very much important from the examination point of view. Our subject matter experts have compiled the solutions in a structured manner so that you can solve all your doubts instantly. Here is a quick summary of the chapter along with some important information that you must know before you start solving the NCERT exercises of the chapter.
Important Topics for NCERT Solutions for Class 8 Maths Chapter 7 – Cubes and Cube Roots Cubes
The term Cube means a solid figure consisting of all equal sides. The solid figure refers to the figures which have 3 dimensions. There are certain cubes that are perfect cubes. These cubes are derived when any number is multiplied three times by itself. Perfect cubes are also known as the cube numbers.
For example: 53= 5 x 5 x 5 = 125. So, this means 125 is a perfect cube. Similarly, 1, 8, 27, 64, 729, 1000, etc., are also perfect cubes.
Did you know that from 1 to 1000, there are only ten perfect cubes!
Given below are some fun facts about the cubes:
- Adding consecutive odd numbers
By adding consecutive odd numbers, we will obtain a cube of a number. For example: 3 + 5= 8 = 23, 7 + 9+ 11 = 27 = 33
- Cubes and their prime factors
In a cube, each prime factor will appear three times. If we take out prime factorisation of any number and each factor appears three times, then that number is a perfect cube. For example: 729= 3 x 3 x 3 x 3 x 3 x 3 . 729 is a perfect cube.
Smallest Multiple That is a Perfect Cube
When any number is not a perfect cube, we will find out the smallest natural number by which the given number must be multiplied or divided, and then we will obtain a perfect cube.
392 = 2 x 2 x 2 x 7 x 7. 392 is not a perfect cube as the number 7 is not in a group of three. To make it a cube we need a 7. 392 x 7 = 2 x 2 x 2 x 7 x 7 x 7 = 2744. So, 7 is the smallest natural number which must be multiplied to 392 to make it a perfect cube.
Cube Roots: it is inverse in operation to that of finding a cube. The symbol of the cube root is ∛. The Cube root of the 8 is 2 i.e. ∛8 = 2.
Cube Root through the Prime Factorisation Method
We can find out the cube root of any number by prime factorisation method. For example: to calculate the cube root of 8000, first carry out its prime factorisation 8000= 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5. ∛8000 = 2 x 2 x 5 = 20.
Cube Root of a Cube Number
In order to find out the cube root of cube number, all you need to do is to follow these simple steps:
- To find the cube root of 857375, first, divide the number into groups of 3 digits. Now, you will have two groups – 857 and 375. The group 375 ends with 5 which means the cube of 375 will also end with 5. Therefore, 5 would be at the one’s/unit’s place of the cube root of 857375.
- For the second group 857, you need to find the cube roots between which this number lies (if the number is not the perfect cube). 93 is 729 and 103 is 1000, and our number 857 lies between the two. So we will take the smaller number that is 729. The unit’s place number of 729 will become the ten’s place number of 857375. So, ∛857375 = 95.
Discussion of Exercises for NCERT Class 8 Maths Chapter 7
The NCERT Solutions for Class 8 Maths Chapter 7 contains 2 exercises- 7.1 and 7.2. Now, let us discuss each of them:
- In the first question, you have to identify whether the numbers given are perfect cube or not
- The second question relates to finding the smallest number which can be multiplied by the given number to obtain a perfect cube.
- The third question is about finding the smallest number which can be divided by the given number to obtain a perfect cube.
- In the fourth question, you have to count the number of cuboids in order to form a cube.
- In the first question, you have to find out the cube root of certain numbers by the method of prime factorisation.
- For your better understanding of the chapter, in the second question, you have to mention true and false.
- The last question relates to finding the cube root of a perfect number/ perfect cube and also finding out the cube root by prime factorisation method.
Benefits of using NCERT Solutions for Class 8 Maths Chapter 7 by Instasolv
To meet your competency level, simple and easy language has been used to explain these important topics in the NCERT Class 8 Maths Chapter 7 Solutions. Instasolv not only simplifies difficult topics with its lucid explanation but also highlights important areas essential from the examination point of view. After referring to our NCERT Solutions for Class 8 Maths Chapter 7, you will be able to solve all the questions relating to Cubes and Cube roots perfectly. This content will not only maximize your academic performance but would also assist you in strengthening your knowledge in the long run.