Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.
Solution:
Given, the number is 9720.
We have to determine if 9720 is a perfect cube or not.
Prime factorization is a way of expressing a number as a product of its prime factors.
A prime number is a number that has exactly two factors, 1 and the number itself.
Using prime factorisation,
So, 9720 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5
We observe that 3 and 5 occur without pairs.
Therefore, 9720 is not a perfect cube.
We have to determine the smallest number by which 9720 should be divided to get a perfect cube.
9720 should be divided by 3 × 3 × 5
3 × 3 × 5 = 45
So, 9720/45 = 216
Factors of 216 = 2 × 2 × 2 × 3 × 3 × 3
Therefore, the smallest number to be divided is 45.
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☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 3 Problem 99
Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube
Summary:
9720 is not a perfect cube. The smallest number by which 9720 should be divided to get a perfect cube is 45.
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