(i) 216
Prime factors of 216 = 2 x 2 x 2 x 3 x 3 x 3
Here all factors are in groups of 3’s (in triplets)
Therefore, 216 is a perfect cube number.
(ii) 128
Prime factors of 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2
Here one factor 2 does not appear in a 3’s group.
Therefore, 128 is not a perfect cube.
(iii) 1000
Prime factors of 1000 = 2 x 2 x 2 x 5 x 5 x 5
Here all factors appear in 3’s group.
Therefore, 1000 is a perfect cube.
(iv) 100
Prime factors of 100 = 2 x 2 x 5 x 5
Here all factors do not appear in 3’s group.
Therefore, 100 is not a perfect cube.
(v) 46656
Prime factors of 46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
Here all factors appear in 3’s group.
Therefore, 46656 is a perfect cube.

Class 8 Maths Chapter 7 Exercise 7.1 Solution in Video

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https://www.tiwariacademy.com/ncert-solutions/class-8/maths/chapter-7/