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

Image of cube root 2744 for cubes and cube roots

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
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
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
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
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
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.