NCERT Class 8 Mathematics Solutions: Chapter 7 – Cubes and Cube Roots Exercise 7.1 Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

Glide to success with Doorsteptutor material for CBSE/Class-8 : get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-8.

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
2216
2108
254
327
39
33
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
2128
264
232
216
28
24
22
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
21000
2500
2250
5125
525
55
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
2100
250
525
55
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
246656
223328
211664
25832
22916
21458
3729
3243
381
327
39
33
1

Prime factors of

Here, all factors appear in 3՚s group.

Therefore, 46656 is a perfect cube.

Developed by: