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# Important Questions for CBSE Class 8 Maths Chapter 7 - Cubes and Cube Roots

Last updated date: 03rd Aug 2024
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## CBSE Class 8 Maths Important Questions for Cubes and Cube Roots - Free PDF Download

CBSE Class 8 Maths Chapter 7 Cubes and Cube Roots Important Questions is an important part of the subject. To understand this chapter well, focus on how the experts have compiled the important questions, realise the context and learn how to solve them. Use these questions as a practice ground and their solutions as a guide for learning specific mathematical skills to score more in the exams.

Get the free PDF download of Important Questions with solutions for CBSE Class 8 Maths Chapter 7 - Cubes and Cube Roots prepared by expert Mathematics teachers from latest edition of CBSE (NCERT) books. Register online for Maths tuition on Vedantu.com to score more marks in your examination.

## Study Important Questions for Class 8 Maths Chapter 7 – Cube and Cube Roots

1. ${8^3} =$___$\times$___$\times$___

Ans: $8 \times 8 \times 8 = 512$

2. $( - 4) \times ( - 4) \times ( - 4) = ?$

Ans: $- 4 \times - 4 \times - 4 = - 64$

3. Say True/False. Is cube of every even number is even?

Ans: True

4. Say true/false. The cube of every odd number is not odd?

Ans:  False, cube of every odd number is odd.

5. ${(3.5)^3} =$ ?

Ans:  $3.5 \times 3.5 \times 3.5 = 12.25 \times 3.5 = 42.875$

6. ${x^3}$ is read as

Ans: $x$ to the power of $3$ or $x$ cube.

7. $\sqrt[3]{{ - {x^3}}} =$ ?

Ans: $\sqrt[3]{{ - {x^3}}} = - {\left( {{x^3}} \right)^{\dfrac{1}{3}}} = - x$

8. $\sqrt[3]{{ab}} = ?$

Ans: $\sqrt[3]{a} \times \sqrt[3]{b}$

9. $\sqrt[3]{{\dfrac{a}{b}}} = ?$

Ans: $\dfrac{{\sqrt[3]{a}}}{{\sqrt[3]{b}}}$

10. A natural number is said to be __________ if it is the cube of some natural number.

Ans: Perfect cube

### Short Answer Questions     2 Marks

11. Show that $192$ is not a perfect cube.

Ans: By prime factorization,

$\sqrt[3]{{192}} = \sqrt[3]{{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times 3}}$

Here, the product cannot be expressed in the form of triplets.

Hence, this is not a perfect cube.

12. Find the cube of $( - 9)$

Ans: ${( - 9)^3} = - 9 \times - 9 \times - 9$

$= 81 \times ( - 9)$

$= - 729$

13. Find the cube of $2\dfrac{2}{3}$

Ans: ${\left( {2\dfrac{2}{3}} \right)^3} = 2\dfrac{2}{3} \times 2\dfrac{2}{3} \times 2\dfrac{2}{3}$

$= \dfrac{8}{3} \times \dfrac{8}{3} \times \dfrac{8}{3}$

$= \dfrac{{512}}{{27}}$

14. Find the cube of $(0.09)$.

Ans: ${(0.09)^3} = 0.09 \times 0.09 \times 0.09$

$= 0.0081 \times 0.09$

$= 0.000729$

15. Show that $4096$ is a perfect cube.

Ans: By prime factorization,

$\sqrt[3]{{4096}} = \sqrt[3]{{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2)\times (2 \times 2 \times 2)}}$

Here, the number can be expressed as the product of triplets.

Hence, a given number is a perfect square.

16. By what least number should $336$ be divided to get a perfect cube?

Ans: By prime factorization,

$\sqrt[3]{{336}} = \sqrt[3]{{(2 \times 2 \times 2) \times 2 \times 3 \times 7}}$

$336$should be divided by $2 \times 3 \times 7 = 42$.

17. By what least number should $675$ multiplied to get a perfect cube?

Ans: By prime factorization,

$\sqrt[3]{{675}} = \sqrt[3]{{(3 \times 3 \times 3) \times 5 \times 5}}$

Hence to make it a perfect cube, we must multiply by $5.$

### Long Answer Questions      4 Marks

18. What is the smallest number by which $2048$ may be multiplied so that the product is a perfect cube?

Ans: By prime factorization,

$\sqrt[3]{{2048}} = \sqrt[3]{{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times 2 \times 2}}$

Clearly $2048$ should be multiplied with $2$ to make perfect cube.

19. Find $\sqrt[3]{{125 \times ( - 343)}}$

Ans: By prime factorization

$= \sqrt[3]{{5 \times 5 \times 5 \times ( - 7) \times ( - 7) \times ( - 7)}}$

$= 5 \times ( - 7)$

$= - 35$

20. $\sqrt[3]{{\dfrac{{8000}}{{1331}}}}$

Ans: $\sqrt[3]{{\dfrac{{8000}}{{1331}}}}$ can be written as $\dfrac{{\sqrt[3]{{8000}}}}{{\sqrt[3]{{1331}}}}$

Calculate each value by prime factorization,

$\sqrt[3]{{8000}} = \sqrt[3]{{(2 \times 2 \times 2) \times (5 \times 5 \times 5) \times (2 \times 2 \times 2)}}$

$\sqrt[3]{{1331}} = \sqrt[3]{{(11 \times 11 \times 11)}}$

Now,

$\sqrt[3]{{\dfrac{{8000}}{{1331}}}} = \sqrt[3]{{\dfrac{{2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 2 \times 2 \times 2}}{{11 \times 11 \times 11}}}}$

$= \dfrac{{2 \times 5 \times 2}}{{11}}$

$= \dfrac{{20}}{{11}}$

### Very Long Answer Questions      5 Marks

21. Find the value of ${31^3}$ by shortcut method.

Ans: Let ${(31)^3} = {(30 + 1)^3}$

We know, ${(a + b)^3} = {a^3} + 3{a^2}b + 3a{b^2} + {b^3}$

$(31){ = ^3}{(30 + 1)^3}$

$= {(30)^3} + 3{(30)^2} + 3(30) + 1$

$= 27000 + (3 \times 900) + 90 + 1$

$= 27000 + 2700 + 90 + 1$

$= 29791$

22. Evaluate $\sqrt[3]{{4913}}$

Ans: By prime factorization,

$17|\underline {4913}$

$17|\underline {289}$

$17|\underline {17}$

$= \sqrt[3]{{4913}}$

$= \sqrt[3]{{17 \times 17 \times 17}}$

$= 17$

23. Find $\sqrt[3]{{ - 13824}}$

Ans: By prime factorization,

$- \sqrt[3]{{13824}} = - \sqrt[3]{{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (3 \times 3 \times 3)}}$

$= - 2 \times 2 \times 2 \times 3$

$= - 4 \times 6$

$= - 24$

24. Evaluate $\sqrt[3]{{512 \times 343}}$

Ans: By prime factorization,

$\sqrt[3]{{512 \times 343}} = \sqrt[3]{{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (7 \times 7 \times 7)}}$

$= 2 \times 2 \times 2 \times 7$

$= 56$

## Significance of CBSE Class 8 Maths Chapter 7 Cubes and Cube Roots Important Questions

Calculating cubes and cube roots requires following specific methods. There are important techniques explained by the CBSE Class 8 Maths Chapter 7 Cubes and Cube Roots. This chapter explains what a cube and the cube root of a number are and how to determine them. The mathematical operations explained in the chapter help students solve the exercise questions easily.

Once the exercises are completed, students can download and solve the important questions compiled by the experts of Vedantu. These questions are based on the latest CBSE syllabus of Class 8 Maths. The experts have covered all the important topics of this chapter while compiling these questions. Hence, these questions will act as the perfect guide to check the preparation level of the students.

The solutions provided with these important questions will also enable students to understand how to approach solving such questions. They will learn the precise stepwise methods to determine cubes and cube roots of different numbers and proceed with their preparation for this chapter.

## Advantages of CBSE Class 8 Maths Chapter 7 Cubes and Cube Roots Important Questions

• The questions have been compiled to cover the entire syllabus of this chapter. The answers have been kept concise and easy to understand. You can avail of these questions and answers in a single file for convenience. You can either download this list of questions or can access it online.

• Resolve doubts related to these important questions instantly with the solutions given. You can rest assured that the answers to all these questions are accurate and can be practised.

• Find the easiest format for answering such questions in the solutions. Follow the same and practise solving these questions at home to develop similar skills. This is how you can excel in developing similar skills and score more in the exams.

Vedantu is a platform that provides free (CBSE)  NCERT Solutions and other study materials for students.  Subjects like Science, Maths, and English will become easy to study if you have access to NCERT Solution for NCERT Solution for Class 8 Science, Maths solutions and solutions of other subjects.

## Download CBSE Class 8 Maths Chapter 7 Cubes and Cube Roots Important Questions PDF

Get the free PDF version of these questions and answers for this chapter. Solve these questions during your practice sessions and become better in this chapter. learn and imbibe the methods of determining cubes and cube roots faster to answer exam questions precisely and to stay ahead of the competition.

## Conclusion

Vedantu's offering of "Important Questions for CBSE Class 8 Maths Chapter 7 - Cubes and Cube Roots" is an invaluable asset for students. These questions are strategically curated to focus on key concepts and problem-solving skills related to cubes and cube roots, aiding in comprehensive exam preparation. Vedantu's commitment to providing these resources enhances accessibility to quality educational materials, empowering students in their academic journey. By offering these important questions, Vedantu not only facilitates better understanding but also promotes excellence in CBSE Math exams. They serve as a targeted tool for honing mathematical abilities and laying a strong foundation for future mathematical learning, reinforcing Vedantu's dedication to education.

## FAQs on Important Questions for CBSE Class 8 Maths Chapter 7 - Cubes and Cube Roots

1. What do you mean by a perfect cube?

An integer identical to another integer raised to the third power is called a perfect cube. Raising a number to the third power is referred to as cubing the number. A perfect cube is a result of multiplying the same integer three times. Thus, from 1 to 100, there are four perfect cubes: 1, 8, 27, and 64. Even though this is a simple concept, adequate practice is required to be well acquainted with cubes and cube roots.

2. What do you mean by cube roots?

Three times multiplied by an integer's cube root gives the original number. Unlike the square root, the cube root , has no domain restriction in real numbers. The radicand can be any real number, and the cube root will yield a real number as a result. Prime factorisation is an efficient and simple way of finding out the cube roots of any given number or checking whether the given number is a perfect cube or not. To learn and understand more about Cube Roots for Class 8 Chapter 7, visit Vedantu.

3. What is the prime factorisation of cube roots?

Prime factorisation is the process of factoring a number in terms of prime numbers, with prime numbers as the factors. In the prime factorisation of a number's cube, each prime factor appears three times. This is the only condition to determine the condition of any cube or cube root. To get the least prime factor of a number, start by dividing it by the smallest prime number, such as 2, then 3, 5, and so on.

4. How are cube roots used in real life?

When solving cubic equations, the cube root is frequently employed. For example, it  may be used to find the dimensions of a three-dimensional object of a given volume. Using cube roots, you may get a more exact measurement of your flat. Cube roots are used in everyday mathematics to calculate the side of a three-dimensional cube when its volume is known, such as in powers and exponents. In metallurgy, cubes and cube roots are utilized to give the iron block a diving form.

5. Where can I avail the Solutions of Class 8 Maths Chapter 7 solutions?

The solutions are easily available on the Vedantu's website.

• Visit the page NCERT Solutions for Class 8 Maths Chapter 7.

• The webpage with Vedantu’s Solutions for Class 8 Maths Chapter 7 will open.