Perfect Cube




A natural number is said to be a perfect cube if it is the cube of some natural number.
In order to check whether the given number is a perfect-cube or not, follow the following procedure:-

1. Obtain the natural number.
2. Express the number as a factor of prime numbers.
3. Group the equal factors in triples.
4. After grouping if no factors are left then the given number is perfect cube, otherwise not.


Example:
1) 256
Solution :
256 = 2 x 128
= 2 x 2 x 64
= 2 x 2 x 2 x 32
= 2 x 2 x 2 x 2 x 16
= 2 x 2 x 2 x 2 x 2 x 8
= 2 x 2 x 2 x 2 x 2 x 2 x 4
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
After grouping the factors of equal triples, 2 x 2 is left.
So, 256 is not a perfect-cube.
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2) 216
Solution :
216 = 2 x 108
= 2 x 2 x 54
= 2 x 2 x 2 x 27
= 2 x 2 x 2 x 3 x 9
= 2 x 2 x 2 x 3 x 3 x 3
We find that the prime factors of 216 can be grouped into triples of equal factor and no factor is left over.
So, 216 is a perfect-cube
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2) 729
Solution :
729 = 3 x 243
= 3 x 3 x 81
= 3 x 3 x 3 x 27
= 3 x 3 x 3 x 3 x 9
= 3 x 3 x 3 x 3 x 3 x 3
We find that the prime factors of 729 can be grouped into triples of equal factor and no factor is left over.
So, 729 is a perfect-cube
Cube and Cube Roots

Cube of Numbers
Perfect Cube
Properties of Cube
Cube by Column method
Cube of Negative numbers
Cube of Rational numbers
Cube Root
Finding cube root by Prime Factorization
Cube root of Rational numbers
Estimating cube root

Cube to Exponents

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