# Concept of Cube Number

## Definition

Cube numbers: Numbers obtained when a number is multiplied by itself three times are known as cube numbers.

## Notes

### Cubes Number:

If a natural number m can be expressed as n3, where n is also a natural number, then m is called the cube number of n.

For Example,
1 = 1 × 1 × 1 = 13; 8 = 2 × 2 × 2 = 23; 27 = 3 × 3 × 3 = 33.

Numbers obtained when a number is multiplied by itself three times are known as cube numbers.

53 = 5 × 5 × 5 = 125, therefore 125 is a cube number.

These are called perfect cubes or cube numbers.

 Number Cube Number Cube 1 1 11 1331 2 8 12 1728 3 27 13 2197 4 64 14 2744 5 125 15 3375 6 216 16 4096 7 343 17 4913 8 512 18 5832 9 729 19 6859 10 1000 20 8000

After observing cube number, we say that

• If a number is odd, then its cube number's unit digit is also odd.

• If a number is even, then its cube number's unit digit is also even.

### Cubes Relation with Cube Numbers:

• Figures which have 3-dimensions are known as solid figures.

• A cube is a solid figure which has all its sides equal.

• For example, To make a bigger cube of unit side. We arrange a total of 27 units to make a cube of 3 units. Similarly, a cube of 5 units will have 125 such unit cubes.

## Example

Find the cube of 17.

173 = 17 × 17 × 17 = 4913.

## Example

Find the cube of (-6).

(-6)3 = (-6) × (-6) × (-6) = -216.

## Example

Find the cube of (-2/5).

(-2/5)^3 = (-2/5) xx (-2/5) xx (-2/5) = -8/125.

## Example

Find the cube of (1.2).

(1.2)3 = 1.2 × 1.2 × 1.2 = 1.728

## Example

Find the cube of (0.02).

(0.02)3 = 0.02 × 0.02 × 0.02 = 0.000008.

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