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**Cubes and Cube Root | Speed Notes**

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**Cube number**: Number obtained when a number is multiplied by itself three times. 2^{3 }= 2 x 2 x 2 = 8, 3^{3 }= 3 x 3 x 3=27, etc.

Numbers like 1729, 4104, 13832, are known as Hardy – Ramanujan Numbers. They

can be expressed as sum of two cubes in two different ways.

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Numbers obtained when a number is multiplied by itself three times are known as cube numbers. For example 1, 8, 27, … etc.

If in the prime factorisation of any number each factor appears three times, then the

number is a perfect cube.

The symbol

denotes cube root. For example

**Perfect Cube: **A natural number is said to be a perfect cube if it is the cube of some natural number. Example: 8 is perfect cube, because there is a natural number 2 such that 8 = 2^{3}, but 18 is not a perfect cube, because there is no natural number whose cube is 18.

The cube of a negative number is always negative.

**Properties of Cube of Number:**

- Cubes of even number are even.
- Cubes of odd numbers are odd.
- The sum of the cubes of first n natural numbers is equal to the square of their sum.
- Cubes of the numbers ending with the digits 0, 1, 4, 5, 6 and 9 end with digits 0, 1, 4, 5, 6 and 9 respectively.
- Cube of the number ending in 2 ends in 8 and cube of the number ending in 8 ends in 2.
- Cube of the number ending in 3 ends in 7 and cube of the number ending in 7

ends in 3.

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