NCERT Solutions
Class 8 Maths
Cubes and Cube Roots

Ex.7.1 Q.1
Which of the following numbers are not perfect cubes:
1. 216
2. 128
3. 1000
4. 100
5. 46656
1. 216
Prime factors of 216 = 2 × 2 × 2 × 3 × 3 × 3
Here all factors are in groups of 3’s (in triplets)
Therefore, 216 is a perfect cube number.
2. 128
Prime factors of 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
Here one factor 2 does not appear in a 3’s group.
Therefore, 128 is not a perfect cube.
3. 1000
Prime factors of 1000 = 2 × 2 × 2 × 3 × 3 × 3
Here all factors appear in 3’s group.
Therefore, 1000 is a perfect cube.
4. 100
Prime factors of 100 = 2 × 2 × 5 × 5
Here all factors do not appear in 3’s group.
Therefore, 100 is not a perfect cube.
5. 46656
Prime factors of 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
Here all factors appear in 3’s group.
Therefore, 46656 is a perfect cube.