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

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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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