Question:
Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.
Solution:
First we have to find out the factors by using prime factorisation method.
So, prime factors of 9720 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5
Now, grouping the prime factors = (2 × 2 × 2) × (3 × 3 × 3) × 3 × 3 × 5
= 23 × 33 × 3 × 3 × 5
Factors 3 and 4 has no pair.
∴9720 is not a perfect cube.
The smallest number it should be divided to get a perfect cube is 3 × 3 × 5 = 45.
Then,
= 9720 ÷ 45
= 216
Factors of 216 = (2 × 2 × 2) × (3 × 3 × 3)
3√216 = 3√((2 × 2 × 2) × (3 × 3 × 3))
= 3√(23 × 32)
= 6