MathsCubes and Cube Roots Class 8 Extra Questions Maths Chapter 7

Cubes and Cube Roots Class 8 Extra Questions Maths Chapter 7

Cubes and Cube Roots Class 8 Extra Questions Maths Chapter 7

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

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

Question 1.
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

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    Question 2.
    Find the cubes of the following:
    (a) 0.3
    (b) 0.8
    (c) .001
    (d) 2 – 0.3
    Sol.
    (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

    Question 3.
    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

    Question 4.
    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

    Question 5.
    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

    Question 6.
    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

    Question 7.
    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

    Question 8.
    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.

    Question 9.
    Using prime factorisation, find the cube root of 5832. (NCERT Exemplar)
    Solution:
    Cubes and Cube Roots NCERT Extra Questions for Class 8 Maths Q9

    Question 10.
    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

    Question 11.
    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

    Question 12.
    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

    Question 13.
    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

    Question 14.
    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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