NCERT Class 8 Mathematics Solutions: Chapter 7 – Cubes and Cube Roots Exercise 7.1 Part 1

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Image of cube root 2744 for cubes and cube roots

Image of Cube Root 2744 for Cubes and Cube Roots

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Question: 1 Which of the following numbers are not perfect cubes:

(i) 216

(ii) 128

(iii) 1000

(iv) 100

(v) 46656

(iv) 100

Answer:

(i) 216

Table shows the factor of 216

2

216

2

108

2

54

3

27

3

9

3

3

1

Prime factors of 216 =

Here all factors are in groups of 3’s (in triplets)

Therefore, 216 is a perfect cube number.

(ii) 128

Table shows the factor of 128

2

128

2

64

2

32

2

16

2

8

2

4

2

2

1

Prime factors of

Here one factor 2 does not appear in a 3’s group.

Therefore, 128 is not a perfect cube.

(iii) 1000

Table shows the factor of 1000

2

1000

2

500

2

250

5

125

5

25

5

5

1

Prime factors of 1000

Here all factors appear in 3’s group.

Therefore, 1000 is not a perfect cube.

(iv) 100

Table shows the factor of 100

2

100

2

50

5

25

5

5

1

Prime factors of 100

Here all factors do not appear in 3’s group.

Therefore, 100 is not a perfect cube.

(v) 46656

Table shows the cube root of 46656

2

46656

2

23328

2

11664

2

5832

2

2916

2

1458

3

729

3

243

3

81

3

27

3

9

3

3

1

Prime factors of

Here, all factors appear in 3’s group.

Therefore, 46656 is a perfect cube.