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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In order to check whether the given number is a perfect-cube or not, follow the following procedure:-

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.

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.

________________________________________________________________

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.

• 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

Home Page