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 ⋅ 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.

15³  =  (10 + 5)³

a = 10, b = 5

(10 + 5)^{3  =}  (10)³ + 5³ + 3(10)5 (10 + 5)

15^{3  =}  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)³  =  (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

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