Cubes and Cube Roots Ncert Solutions
NCERT Solutions Class 8 Maths Chapter 7 Cubes and Cube Roots – Here are all the NCERT solutions for Class 8 Maths Chapter 7. This solution contains questions, answers, images, explanations of the complete chapter 7 titled Cubes and Cube Roots of Maths taught in class 8. If you are a student of class 8 who is using NCERT Textbook to study Maths, then you must come across chapter 7 Cubes and Cube Roots. After you have studied lesson, you must be looking for answers of its questions. Here you can get complete NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots in one place.
NCERT Solutions Class 8 Maths Chapter 7 Cubes and Cube Roots
Subscribe For Latest Updates
Here on AglaSem Schools, you can access to NCERT Book Solutions in free pdf for Maths for Class 8 so that you can refer them as and when required. The NCERT Solutions to the questions after every unit of NCERT textbooks aimed at helping students solving difficult questions.
For a better understanding of this chapter, you should also see summary of Chapter 7 Cubes and Cube Roots , Maths, Class 8.
| Class | 8 |
| Subject | Maths |
| Book | Mathematics |
| Chapter Number | 7 |
| Chapter Name | Cubes and Cube Roots |
NCERT Solutions Class 8 Maths chapter 7 Cubes and Cube Roots
Class 8, Maths chapter 7, Cubes and Cube Roots solutions are given below in PDF format. You can view them online or download PDF file for future use.
Cubes and Cube Roots Download
NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Download
Did you find NCERT Solutions Class 8 Maths chapter 7 Cubes and Cube Roots helpful? If yes, please comment below. Also please like, and share it with your friends!
NCERT Solutions Class 8 Maths chapter 7 Cubes and Cube Roots- Video
You can also watch the video solutions of NCERT Class8 Maths chapter 7 Cubes and Cube Roots here.
If you liked the video, please subscribe to our YouTube channel so that you can get more such interesting and useful study resources.
Download NCERT Solutions Class 8 Maths chapter 7 Cubes and Cube Roots In PDF Format
You can also download here the NCERT Solutions Class 8 Maths chapter 7 Cubes and Cube Roots in PDF format.
Click Here to download NCERT Solutions for Class 8 Maths chapter 7 Cubes and Cube Roots
Question & Answer
Q.1: Find the one's digit of the cube of each of the following numbers. (i) 3331 (ii) 8888 (iii) 149 (iv) 1005 (v) 1024 (vi) 77 (vii) 5022 (viii) 53 Q.2: Express the following numbers as the sum of odd numbers using the above pattern? (a) \( 6^{3} \) (b) \( 8^{3} \) (c) \( 7^{3} \) Consider the following pattern. \( 2^{3}-1^{3}=1+2 \times 1 \times 3 \) \( 3^{3}-2^{3}=1+3 \times 2 \times 3 \) \( 4^{3}-3^{3}=1+4 \times 3 \times 3 \) Using the above pattern, find the value of the following. (i) \( 7^{3}-6^{3} \) (ii) \( 12^{3}-11^{3} \) (iii) \( 20^{3}-19^{3} \) (iv) \( 51^{3}-50^{3} \) Q.3: Which of the following are perfect cubes? 1. 400 2. 3375 3. 8000 4. 15625 5. 9000 6. 6859 7. 2025 8. 10648 Q.4: Which of the following numbers are not perfect cubes? (i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656 Ans : (i) The prime factorisation of 216 is as follows:
\( 216=2 \times 2 \times 2 \times 3 \times 3 \times 3=2^{3} \times 3^{3} \) Here, as each prime factor is appearing as times as a perfect multiple of 3, therefore, 216 is a perfect cube. (ii) The prime factorisation of 128 is as follows:
128 = 2 x 2 x 2 x 2 x 2 x 2 x 2 Here, each prime factor is not appearing as many times as a perfect multiple of 3. One is 2 remaining after grouping the triplets of 2, 128 is not a perfect cube. (iii) The prime factorisation of 1000 is as follows:
1000 = 2 x 2 x 2 x 5 x 5 x 5 Here, as each prime factor is appearing as many times as a perfect multiple of 3, therefore, 1000 is a perfect cube. (iv) The prime factorisation of 100 is as follows:
100 = 2 x 2 x 5 x 5 Here, each prime factor is not appearing as many times as a perfect multiple of 3. Two 2s and two 5s are remaining after grcmping the triplets. Therefore, 100 is not a perfect cube. (v) The prime factorisation of 46656 is as follows:
46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 Here, as each prime factor is appearing as many times as a perfect multiple of 3, therefore, 46656 is a perfect cube.
Q.5: Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100 Ans : (i) 243 = 3 x 3 x 3 x 3 x 3 Here, two 3s are left which are not in a triplet. To make 243 a cube, one more 3 is required. In that case, 243 x 3 = 3 x 3 x 3 x 3 x 3 x 3 = 729 is a perfect cube. Hence, the smallest natural number by which 243 should be multiplied to make it a perfect cube is 3. (ii) 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 Here, two 2s are left which are not in a triplet. To make 256 a cube, one more 2 is required. Then, we obtain 256 x 2 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512 is a perfect cube. Hence, the smallest natural number by which 256 should be multiplied to make it a perfect cube is 2. (iii) 72 = 2 x 2 x 2 x 3 x 3 Here, two 3s are left which are not in a triplet. To make 72 a cube, one more 3 is required. Then, we obtain, 72 x 3 = 2 x 2 x 2 x 3 x 3 x 3 = 216 is a perfect cube. Hence, the smallest natural number by which 72 should be multiplied to make it a perfect cube is 3. (iv) 675 = 3 x 3 x 3 x 5 x 5 Here, two 5s are left which are not in triplet. To make 675 a cube, one more 5 is required. Then, we obtain 675 x 5 = 3 x 3 x 3 x 5 x 5 x 5 = 3756 is a perfect cube. Hence , the smallest natural number by which 675 should be multiplied to make it a perfect cube is 5. (v) 100 = 2 x 2 x 5 x 5 Here, two 2s and two 5s are left which are not in a triplet. To make 100 a cube, we require one more 2 and one more 5. Then, we obtain 100 x 2 x 5 = 2 x 2 x 2 x 5 x 5 x 5 = 1000 is a perfect cube. Hence, the smallest natural number by which 100 should be multiplied to make it a perfect cube is 2 x 5 = 10
NCERT / CBSE Book for Class 8 Maths
You can download the NCERT Book for Class 8 Maths in PDF format for free. Otherwise you can also buy it easily online.
- Click here for NCERT Book for Class 8 Maths
- Click here to buy NCERT Book for Class 8 Maths
All NCERT Solutions Class 8
- NCERT Solutions for Class 8 English
- NCERT Solutions for Class 8 Hindi
- NCERT Solutions for Class 8 Maths
- NCERT Solutions for Class 8 Science
- NCERT Solutions for Class 8 Social Science
- NCERT Solutions for Class 8 Sanskrit
All NCERT Solutions
You can also check out NCERT Solutions of other classes here. Click on the class number below to go to relevant NCERT Solutions of Class 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
| Class 1 | Class 2 | Class 3 |
| Class 4 | Class 5 | Class 6 |
| Class 7 | Class 8 | Class 9 |
| Class 10 | Class 11 | Class 12 |
Download the NCERT Solutions app for quick access to NCERT Solutions Class 8 Maths Chapter 7 Cubes and Cube Roots. It will help you stay updated with relevant study material to help you top your class!
Previous Next
To get fastest exam alerts and government job alerts in India, join our Telegram channel.
Cubes and Cube Roots Ncert Solutions
Source: https://schools.aglasem.com/ncert-solutions-class-8-maths-chapter-7/
0 Response to "Cubes and Cube Roots Ncert Solutions"
Post a Comment