**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 = 3^{3}

(ii) 5 **⋅ **5 **⋅** 5 = 5^{3}

In example (ii) 5^{3} 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

15^{3}

**Solution :**

To find the value of 15^{3}, we have to multiply 15 three times.

15^{3} = 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} = a^{3} + b^{3 }+ 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^{3 } = (10 + 5)^{3}

a = 10, b = 5

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

15^{3 = }1000^{ }+ 125 + 150 (15)

= 1000 + 125 + 2250

= 3375

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

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

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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