NCERT Solutions
Class 8 Maths
Cubes and Cube Roots

Ex.7.1 Q.2
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:
1. 243
2. 256
3. 72
4. 675
5. 100
1. 243
Prime factors of 243 = 3 × 3 × 3 × 3 × 3
Here, 3 does not appear in 3’s group.
Therefore, 243 must be multiplied by 3 to make it a perfect cube.
2. 256
Prime factors of 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Here one factor 2 is required to make a 3’s group.
Therefore, 256 must be multiplied by 2 to make it a perfect cube.
3. 72
Prime factors of 72 = 2 × 2 × 2 × 3 × 3
Here 3 does not appear in 3’s group.
Therefore, 72 must be multiplied by 3 to make it a perfect cube
4. 675
Prime factors of 675 = 3 × 3 × 3 × 5 × 5
Here factor 5 does not appear in 3’s group.
Therefore 675 must be multiplied by 3 to make it a perfect cube.
5. 100
Prime factors of 100 = 2 × 2 × 5 × 5
Here factor 2 and 5 both do not appear in 3’s group.
Therefore 100 must be multiplied by 2 × 5 = 10 to
make it a perfect cube.