**What is a cube in Math?**

If a number is multiplied three times by itself, the result we get is called the cube of a number.

To represent the cube of a number, 3 is written a little up to the right of the value.

as:

x^{3}

Here **3** is the exponent of ‘x’, and usually read as** ‘x cubed’.**

**How to Find the cube of a number?**

For a given number ‘n’, we say, a cube of * n = n × n × n,* shown as

n³

**Examples:**

**3 ^{3} = 3*3*3 = 27**

The cube of 3 is 27.

**4 ^{3} = 4*4*4 = 64**

The cube of 4 is 64.

**What is a perfect cube?**

A perfect cube is a resultant number that is the cube of any number.

**Example:**

64 is the perfect cube as

64 = 4*4*4 = 4^{3}

Other Examples of Perfect Cube are; 1, 8, 27, 64, 125 etc.

*A number must be a perfect cube if it can be represented as the product of triplets of the same factors.*

**Cube of Negative Numbers**

The resultant of the cube of a negative number is also a negative number.

**Example:**

**(-3)**^{3}= (-3)*(-3)*(-3) = -27

** **

**(-4)3 = (-4)*(-4)*(-4) = -64**

**Cube of Rational Numbers**

We have a rational number **p/q **and **q****0,**then

(p/q)^{3}= (p*p*p)/(q*q*q)

= p^{3}/q^{3}

So,

**(p/q) ^{3} = p^{3}/q^{3}**

**Example:**

**(5/4)**^{3}= 5^{3}/4^{3}= 125/64

** **

**(3/2)**^{3}= 3^{3}/2^{3}= 27/8

**Some Features of Cube of Numbers**

The resultant of the cube of Even Natural numbers is also an even number.

**Example:**

**2 ^{3 }= 8**

**4 ^{3} = 64**

**6 ^{3} = 216**

The resultant of the cube of Odd Natural numbers is also an odd number.

**Example:**

**1 ^{3} = 1**

**3 ^{3} = 27**

**5 ^{3 }= 125**

**What is Cube Root?**

The reverse of taking a cube of a number is basically calculating the cube root.

The cube root of any number ‘n’ can be expressed as

** **

**Example:**

**4 ^{3} = 64**

Or

** = 4**

In this example, the cube root of 64 is 4.

**Cube Root of a negative number:**

It is possible to calculate the cube root of a negative number. We can easily calculate the cube root of any number as follows:

**Example:**

**-64 = (-4) ^{3}**

** = -4**

In this example, the cube root of -64 is -4.

**Cube Root of a Rational Number:**

We have a rational number of the form p/q and q=0. The following example will help you to understand.

**Example:**

Cube Root of

So, the cube root of is