Worked out examples
Example 1:
Check whether 10648 is a perfect cube or not ?
Sol:
Resolving 10648 into prime factors, we get
10648
=
(2 × 2 × 2) × (11 × 11 × 11)
=
2
3
× 11
3
=
(2 × 11)
3
=
(22)
3
Thus, 10648 is a perfect cube and it is the cube of 22.
Example 2:
Check whether 960 is a perfect cube or not ?
Sol:
Resolving 960 into prime factors, we get
960 = (2 × 2 × 2) × (2 × 2 × 2) × 3 × 5
Clearly, 960 is not a perfect cube
Example 3:
Find the smallest number by which 864 be multiplied so that the product is a perfect cube?
Sol:
Resolving 960 into prime factors, we get
864 = (2 × 2 × 2) × 2 × 2 × (3 × 3 × 3)
Clearly, to make 864 a perfect cube it must be multiplied by 2
Example 4:
Find the cube root of 9261
Sol:
Resolving 960 into prime factors, we get
9261 = (3 × 3 × 3) × (7 × 7 × 7)
Clearly, 960 is not a perfect cube
Cube root of 9261 = 3 × 7 = 21