The students can access the NCERT Solutions for Exercise 7.2 of Class 8, Chapter 7, Cubes and Cube Roots, in this article. The solutions in PDF format, which is available here, can be downloaded for free. The NCERT solutions for Exercise 7.2 of Class 8 are prepared by the subject experts at BYJU’S in such a way that going through these solutions will help students get rid of all the doubts related to the method of finding out the cube roots.
The NCERT textbook provides plenty of questions for the students to solve and practise. The NCERT Solutions for Class 8 Maths helps the students in understanding the most relevant method of answering a question. This way, the students get a clear idea of the concept each time they solve the questions present in the NCERT textbook.
NCERT Solutions for Class 8 Maths Chapter 7 – Cubes and Cube Roots Exercise 7.2
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Exercise 7.1 Solutions 4 Questions (4 Short Answer Questions)
Access Answers to NCERT Class 8 Maths Chapter 7 – Cubes and Cube Roots Exercise 7.2 Page Number 275
1. Find the cube root of each of the following numbers by the prime factorisation method.
(i) 64
Solution:
64 = 2×2×2×2×2×2
By grouping the factors in triplets of equal factors, 64 = (2×2×2)×(2×2×2)
Here, 64 can be grouped into triplets of equal factors,
∴ 64 = 2×2 = 4
Hence, 4 is the cube root of 64.
(ii) 512
Solution:
512 = 2×2×2×2×2×2×2×2×2
By grouping the factors in triplets of equal factors, 512 = (2×2×2)×(2×2×2)×(2×2×2)
Here, 512 can be grouped into triplets of equal factors,
∴ 512 = 2×2×2 = 8
Hence, 8 is the cube root of 512.
(iii) 10648
Solution:
10648 = 2×2×2×11×11×11
By grouping the factors in triplets of equal factors, 10648 = (2×2×2)×(11×11×11)
Here, 10648 can be grouped into triplets of equal factors,
∴ 10648 = 2 ×11 = 22
Hence, 22 is the cube root of 10648.
(iv) 27000
Solution:
27000 = 2×2×2×3×3×3×3×5×5×5
By grouping the factors in triplets of equal factors, 27000 = (2×2×2)×(3×3×3)×(5×5×5)
Here, 27000 can be grouped into triplets of equal factors,
∴ 27000 = (2×3×5) = 30
Hence, 30 is the cube root of 27000.
(v) 15625
Solution:
15625 = 5×5×5×5×5×5
By grouping the factors in triplets of equal factors, 15625 = (5×5×5)×(5×5×5)
Here, 15625 can be grouped into triplets of equal factors,
∴ 15625 = (5×5) = 25
Hence, 25 is the cube root of 15625.
(vi) 13824
Solution:
13824 = 2×2×2×2×2×2×2×2×2×3×3×3
By grouping the factors in triplets of equal factors,
13824 = (2×2×2)×(2×2×2)×(2×2×2)×(3×3×3)
Here, 13824 can be grouped into triplets of equal factors,
∴ 13824 = (2×2× 2×3) = 24
Hence, 24 is the cube root of 13824.
(vii) 110592
Solution:
110592 = 2×2×2×2×2×2×2×2×2×2×2×2×3×3×3
By grouping the factors in triplets of equal factors,
110592 = (2×2×2)×(2×2×2)×(2×2×2)×(2×2×2)×(3×3×3)
Here, 110592 can be grouped into triplets of equal factors,
∴ 110592 = (2×2×2×2 × 3) = 48
Hence, 48 is the cube root of 110592.
(viii) 46656
Solution:
46656 = 2×2×2×2×2×2×3×3×3×3×3×3
By grouping the factors in triplets of equal factors,
46656 = (2×2×2)×(2×2×2)×(3×3×3)×(3×3×3)
Here, 46656 can be grouped into triplets of equal factors,
∴ 46656 = (2×2×3×3) = 36
Hence, 36 is the cube root of 46656.
(ix) 175616
Solution:
175616 = 2×2×2×2×2×2×2×2×2×7×7×7
By grouping the factors in triplets of equal factors,
175616 = (2×2×2)×(2×2×2)×(2×2×2)×(7×7×7)
Here, 175616 can be grouped into triplets of equal factors,
∴ 175616 = (2×2×2×7) = 56
Hence, 56 is the cube root of 175616.
(x) 91125
Solution:
91125 = 3×3×3×3×3×3×3×5×5×5
By grouping the factors in triplets of equal factors, 91125 = (3×3×3)×(3×3×3)×(5×5×5)
Here, 91125 can be grouped into triplets of equal factors,
∴ 91125 = (3×3×5) = 45
Hence, 45 is the cube root of 91125.
2. State true or false.
(i) Cube of any odd number is even.
Solution:
False
(ii) A perfect cube does not end with two zeros.
Solution:
True
(iii) If the square of a number ends with 5, then its cube ends with 25.
Solution:
False
(iv) There is no perfect cube which ends with 8.
Solution:
False
(v) The cube of a two-digit number may be a three-digit number.
Solution:
False
(vi) The cube of a two-digit number may have seven or more digits.
Solution:
False
(vii) The cube of a single-digit number may be a single-digit number.
Solution:
True
3. You are told that 1,331 is a perfect cube. Can you guess without factorisation what its cube root is? Similarly, guess the cube roots of 4913, 12167, and 32768.
Solution:
(i) 1,331
By grouping the digits, we get 1 and 331
We know that since the unit digit of the cube is 1, the unit digit of the cube root is 1.
∴ We get 1 as the unit digit of the cube root of 1331.
The cube of 1 matches the number of the second group.
∴ The ten’s digit of our cube root is taken as the unit place of the smallest number.
We know that the unit’s digit of the cube of a number having digit as unit’s place 1 is 1.
∴ ∛1331 = 11
(ii) 4913
By grouping the digits, we get 4 and 913
We know that since the unit digit of the cube is 3, the unit digit of the cube root is 7.
∴ we get 7 as unit digit of the cube root of 4913. We know 13 = 1 and 23 = 8 , 1 > 4 > 8.
Thus, 1 is taken as the ten-digit of the cube root.
∴ ∛4913 = 17
(iii) 12167
By grouping the digits, we get 12 and 167.
We know that since the unit digit of the cube is 7, the unit digit of the cube root is 3.
∴ 3 is the unit digit of the cube root of 12167. We know 23 = 8 and 33 = 27, 8 > 12 > 27.
Thus, 2 is taken as the ten-digit of the cube root.
∴ ∛12167= 23
(iv) 32768
By grouping the digits, we get 32 and 768.
We know that since the unit digit of the cube is 8, the unit digit of the cube root is 2.
∴ 2 is the unit digit of the cube root of 32768. We know 33 = 27 and 43 = 64 , 27 > 32 > 64.
Thus, 3 is taken as the ten-digit of the cube root.
∴ ∛32768= 32
In the second exercise of Class 8 Maths Chapter 7 – Cubes and Cube Roots, students will solve questions related to finding the cube root of different numbers. There are 3 questions in Exercise 7.2 of Class 8. In the exercise, the first question contains ten sub-questions in which the cube roots of the given numbers have to be found. The second question is a true or false question containing seven sub-questions, which can be answered based on a student’s understanding of the topic. The third question is again a question in which the students are asked to guess the cube root of the numbers given.
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