# 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:-

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.

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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.

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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.

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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.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.**________________________________________________________________

**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**________________________________________________________________

**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 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

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