MathsExtra Questions – Cubes and Cube Roots Class 8 Maths Chapter 7

Extra Questions – Cubes and Cube Roots Class 8 Maths Chapter 7

Cube and cube roots are fundamental concepts in Class 8 maths. These concepts help us solve problems by finding the cube of a number and the cube root of a number. In this section, we have extra questions on cube and cube roots to help you practice and improve your skills.

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    These extra questions Cube and cube roots in Class 8 maths are designed to be challenging yet manageable, allowing you to develop your critical thinking and problem-solving skills. By working through these questions, you will gain a deeper understanding of the importance of cube and cube roots class 8 extra questions in real-life applications and develop a strong foundation for future mathematical studies.

    Extra Questions for Class 8 Maths Chapter 7 Cubes and Cube Roots

    Explore the concepts of extra questions cubes and cube roots for Class 8. These concepts are crucial for solving various mathematical problems. Here, we have extra questions to help you practice and improve your skills in finding cubes and cube roots.

    Cubes and Cube Roots Class 8 Extra Questions Very Short Answer Type

    Ques: Find the cubes of the following:

    (a) 12

    (b) -6

    (c) \(\frac { 2 }{ 3 }\)

    (d) \(\frac { -5 }{ 6 }\)

    Solution:

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q1

    Ques: Find the cubes of the following:

    (a) 0.3

    (b) 0.8

    (c) .001

    (d) 2 – 0.3

    Solution.

    (a) (0.3)3 = 0.3 × 0.3 × 0.3 = 0.027

    (b) (0.8)3 = 0.8 × 0.8 × 0.8 = 0.512

    (c) (0.001)3 = (0.001) × (0.001) × (0.001) = 0.000000001

    (d) (2 – 0.3)3 = (1.7)3 = 1.7 × 1.7 × 1.7 = 4.913

    Ques: Is 135 a perfect cube?

    Solution:

    Prime factorisation of 135, is:

    135 = 3 × 3 × 3 × 5

    We find that on making triplet, the number 5 does not make a group of the triplet.

    Hence, 135 is not a perfect cube.

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q3

    Ques: Find the cube roots of the following:

    (a) 1728

    (b) 3375

    Solution:

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q4

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q4.1

    Ques: Examine if (i) 200 (ii) 864 are perfect cubes.

    Solution:

    (i) 200 = 2 × 2 × 2 × 5 × 5

    If we form triplet of equal factors, the number 2 forms a group of three whereas 5 does not do it.

    Therefore, 200 is not a perfect cube.

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q5

    (ii) We have 864 = 2 × 2 × 2 × 2 × 2

    If we form triplet of equal factors, the number 2 and 3 form a group of three whereas another group of 2’s does not do so.

    Therefore, 864 is not a perfect cube.

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q5.1

    Ques: Find the smallest number by which 1323 may be multiplied so that the product is a perfect cube.

    Solution:

    1323 = 3 × 3 × 3 × 7 × 7

    Since we required one more 7 to make a triplet of 7.

    Therefore 7 is the smallest number by which 1323 may be multiplied to make it a perfect cube.

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q6

    Ques: What is the smallest number by which 2916 should be divided so that the quotient is a perfect cube?

    Solution:

    Prime factorisation of

    2916 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

    Since we required one more 2 to make a triplet

    Therefore, the required smallest number by which 2916 should be divided to make it a perfect cube is 2 × 2 = 4, i.e., 2916 ÷ 4 = 729 which is a perfect cube.

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q7

    Ques: Check whether 1728 is a perfect cube by using prime factorisation. (NCERT Exemplar)

    Solution:

    Prime factorisation of 1728 is

    1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

    Since all prime factors can be grouped in triplets.

    Therefore, 1728 is a perfect cube.

    Ques: Using prime factorisation, find the cube root of 5832. (NCERT Exemplar)

    Solution:

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q9

    Ques:

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q10

    Solution:

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q10.1

    Cubes and Cube Roots Class 8 Extra Questions Short Answers Type

    Ques:
    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q11
    Solution:
    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q11.1
    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q11.2

    Ques: Find the cube roots of

    (i) 4\(\frac { 12 }{ 125 }\)

    (ii) -0.729

    Solution:

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q12

    Ques: Express the following numbers as the sum of odd numbers using the given pattern
    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q13
    Solution:

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q13.1

    Ques: Observe the following pattern and complete the blank spaces.
    13 = 1
    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q14

    Solution:

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q14.1

    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q14.2

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