# HOW TO FIND CUBE OF A NUMBER

## About "How to find cube of a number"

How to find cube of a number ?

When a number multiplied by itself three times are called cube of a number.

It is denoted by a number raised to the power 3.

For example :

(i) 3 ⋅  3  =  33

(ii) 5 5  5 =  53

In example (ii) 53 is read as 5 to the power of 3 (or) 5 raised to the power 3 (or) 5 cube. 125 is known as the cube of 5.

Similarly, 8 and 64 are the cubes of 2 and 4 respectively.

Let us look into some example problems to understand how to find cube of a number.

Example 1 :

Find the value of following

153

Solution :

To find the value of 153, we have to multiply 15 three times.

153  =  15 ⋅ 15 ⋅ 15

=  225 ⋅ 15

=  3375

Instead of multiplying the base three times, we may obtain the same answer by using the algebraic identity.

(a + b)3  =  a3 + b3 + 3ab(a + b)

Let us workout the same problem in this method.

Step 1 :

To use this method, we have to show the given number as the sum of numbers nearest of 10's or 100's.

Step 2 :

By comparing this with the algebraic identity, we may find the answer.

15 =  (10 + 5)3

a = 10, b = 5

(10 + 5)3  =  (10)3 + 53 + 3(10)5 (10 + 5)

153  =  1000 + 125 + 150 (15)

=  1000 + 125 + 2250

=  3375

## Cube of fraction

To find the cube of fraction, we have to find the cube of numerator and denominator separately.

Otherwise, we may multiply the fraction three times itself.

Example 2 :

Find the cube of the fraction 3/4

Solution :

(3/4)3  =  (3/4)  (3/4)  (3/4)

Product of numerators  =  27

Product of denominators  =  64

Hence (3/4)3  =  27/64

## Cube of decimal numbers

To find cube of decimal number, we may convert the given decimal as fraction, by multiplying the decimal by 10, 100, etc.

Example 3 :

Find the value of following (1.2)3

Solution :

(1.2) =  (1.2 ⋅ (10/10))3

=  (12/10)3

=  (12/10) ⋅ (12/10)  ⋅  (12/10)

=  (12 ⋅ 12 ⋅ 12)/(10 ⋅ 10 ⋅ 10)

=  (6 ⋅ 6 ⋅ 6)/(5 ⋅ 5 ⋅ 5)

=  216/125

After having gone through the stuff given above, we hope that the students would have understood "How to find cube of a number"

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