Class 8 Exam  >  Class 8 Notes  >  Mathematics (Maths) Class 8  >  NCERT Solutions: Cubes & Cube Roots - 2 (Exercise 6.2)

NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

Exercise 6.2

Q1:  Find the cube root of each of the following numbers by prime factorisation method. 

(i)  64

Sol: 64 = 2 × 2 × 2 × 2 × 2 × 2
By grouping the factors in triplets of equal factors, 64 = (2 × 2) x (2 × 2) × (2 × 2)


NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

Here, 64 can be grouped into triplets of equal factors.
∴ 64 = (2 x 2)3 = 43
Hence, 4 is the cube root of 64.


(ii)  512

Sol: 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)NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

Here, 512 can be grouped into triplets of equal factors.
∴ 512 = (2 × 2 × 2)3  = 83
Hence, 8 is the cube root of 512.

(iii) 10648

Sol: 10648 = 2 × 2 × 2 × 11 × 11 × 11
By grouping the factors in triplets of equal factors, 10648 = (2 × 2 × 2) × (11 × 11 × 11)NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

Here, 10648 can be grouped into triplets of equal factors.
∴ 10648 = (2 × 2 x 2) x (11 x 11 x 11) = 23 x 113 = (22)3
Hence, 22 is the cube root of 10648.

(iv) 27000

Sol: 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)NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

Here, 27000 can be grouped into triplets of equal factors.
∴ 27000 = (2 × 3 × 5)3 = 303
Hence, 30 is the cube root of 27000.

(v) 15625

Sol: 15625 = 5 × 5 × 5 × 5 × 5 × 5
By grouping the factors in triplets of equal factors, 15625 = (5 × 5 × 5) × (5 × 5 × 5)NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

Here, 15625 can be grouped into triplets of equal factors.
∴ 15625 = (5 × 5)3 = 253
Hence, 25 is the cube root of 15625.

(vi) 13824

Sol: 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)NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

Here, 13824 can be grouped into triplets of equal factors.
∴ 13824 = (2 × 2 × 2 × 3)3 = 243
Hence, 24 is the cube root of 13824.

(vii) 110592

Sol: 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)NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

Here, 110592 can be grouped into triplets of equal factors.
∴ 110592 = (2 × 2 × 2 × 2 × 3)3 = 483
Hence, 48 is the cube root of 110592.

(viii) 46656

Sol: 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)NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

Here, 46656 can be grouped into triplets of equal factors.
∴ 46656 = (2 × 2 × 3 × 3)= 363
Hence, 36 is the cube root of 46656.

(ix) 175616

Sol: 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)NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

Here, 175616 can be grouped into triplets of equal factors.
∴ 175616 = (2×2×2×7)3 = 563
Hence, 56 is the cube root of 175616.

(x) 91125

Sol: 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)NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

Here, 91125 can be grouped into triplets of equal factors.
∴ 91125 = (3 × 3 × 5)= 453
Hence, 45 is the cube root of 91125.

Q2: State True or False

(i) Cube of any odd number is even.

Ans: False 

(ii) A perfect cube does not end with two zeros.

Ans: True

(iii) If square of a number ends with 5, then its cube ends with 25.

Ans: False 

(iv) There is no perfect cube which ends with 8.

Ans: False 

(v) The cube of a two digit number may be a three digit number.

Ans: False 

(vi) The cube of a two digit number may have seven or more digits.

Ans: False 

(vii) The cube of a single digit number may be a single digit number.

Ans: True


Deleted Questions from NCERT

Question: You are told that 1,331 is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768.

Solution:

(i) Separating the given number (1331) into two groups:

1331 → 1 and 331

∵ 331 end in 1.

∴ Unit’s digit of the cube root = 1

∵ 13 = 1 and ∛1 = 1

∴ Ten’s digit of the cube root = 1 

∛1331 = 11

(ii) Separating the given number (4913) in two groups:

4913 → 4 and 913

Unit’s digits:

∵ Unit’s digit in 913 is 3.

∴ Unit’s digit of the cube root = 7

[73 = 343; which ends in 3]

Ten’s digit:

∵ 13 = 1, 23 = 8

and 1 < 4 < 8

i.e. 1< 4 < 23

∴ The ten’s digit of the cube root is 1.

∛4913 = 17

(iii) Separating 12167 in two groups:

12167 → 12 and 167

Unit’s digit:

∵ 167 is ending in 7 and cube of a number ending in 3 ends in 7.

∴ The unit’s digit of the cube root = 3

Ten’s digit:

∵ 23 = 8 and 33 = 27

Also, 8 < 12 < 27

or 23 < 12 < 32

∴ The tens digit of the cube root can be 2.

Thus,  ∛12167 = 23.

(iv) Separating 32768 in two groups:

32768 → 32 and 786

Unit’s digit:

768 will guess the unit’s digit in the cube root.

∵ 768 ends in 8.

∴ Unit’s digit in the cube root = 2

Ten’s digit:

∵ 33 = 27 and 43 – 64

Also, 27 < 32 < 64

or 33 < 32 < 43

∴ The ten’s digit of the cube root = 3.

Thus, ∛32768 = 32

The document NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2) is a part of the Class 8 Course Mathematics (Maths) Class 8.
All you need of Class 8 at this link: Class 8
79 videos|408 docs|31 tests

Top Courses for Class 8

FAQs on NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

1. What is a cube and what are its properties?
Ans. A cube is a three-dimensional solid object with six square faces, twelve edges, and eight vertices. Some of the properties of a cube are: - All the faces of a cube are congruent and square in shape. - The opposite faces of a cube are parallel and equal in size. - The length of each edge of a cube is equal. - The sum of the angles formed at each vertex of a cube is 360 degrees.
2. How to calculate the volume of a cube?
Ans. The volume of a cube can be calculated by using the formula V = a³, where "a" represents the length of one edge of the cube. To find the volume, simply cube the length of the edge.
3. What is a cube root and how to find it?
Ans. A cube root is a number that, when multiplied by itself three times, gives the original number. To find the cube root of a number, we can use the prime factorization method. We express the number as a product of prime factors and take out the prime factors in groups of three. The remaining factors are multiplied together to get the cube root.
4. How to find the surface area of a cube?
Ans. The surface area of a cube can be calculated by using the formula SA = 6a², where "a" represents the length of one edge of the cube. To find the surface area, simply square the length of the edge and multiply it by 6.
5. How are cubes used in real-life applications?
Ans. Cubes are used in various real-life applications, such as: - Packaging: Cubes are used as basic shapes for packaging boxes, ensuring efficient use of space. - Architecture: Cubes are used as building blocks in construction, creating visually appealing structures. - Mathematics: Cubes are used in mathematical calculations and formulas, helping to solve problems in geometry and algebra. - Gaming: Cubes are used in puzzle games, such as Rubik's Cube, providing entertainment and challenging the mind.
79 videos|408 docs|31 tests
Download as PDF
Explore Courses for Class 8 exam

Top Courses for Class 8

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Extra Questions

,

Sample Paper

,

MCQs

,

NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

,

mock tests for examination

,

pdf

,

NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

,

shortcuts and tricks

,

practice quizzes

,

Free

,

Semester Notes

,

past year papers

,

Exam

,

ppt

,

Important questions

,

Previous Year Questions with Solutions

,

Objective type Questions

,

study material

,

video lectures

,

Viva Questions

,

Summary

,

NCERT Solutions for Class 8 Maths - Cubes and Cube Roots - 2 (Exercise 6.2)

;