NCERT Solutions
Class 8 Maths
Cubes and Cube Roots

Ex.7.1 Q.3
Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:
1. 81
2. 128
3. 135
4. 192
5. 704
1. 81
Prime factors of 81 = 3 × 3 × 3 × 3
Here one factor 3 is not grouped in triplets.
Therefore 81 must be divided by 3 to make it a perfect cube.
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 must be divided by 2 to make it a perfect cube.
3. 135
Prime factors of 135 = 3 × 3 × 3 × 5
Here one factor 5 does not appear in a triplet.
Therefore, 135 must be divided by 5 to make it a perfect cube.
4. 192
Prime factors of 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3
Here one factor 3 does not appear in a triplet.
Therefore, 192 must be divided by 3 to make it a perfect cube.
5. 704
Prime factors of 704 = 2 × 2 × 2 × 2 × 2 × 2 × 11
Here one factor 11 does not appear in a triplet.
Therefore, 704 must be divided by 11 to make it a perfect cube.