cube-root-rational

Math Cube and Cube Root: Explained with Examples

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:

x3

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

Examples:

33 = 3*3*3 = 27

The cube of 3 is 27.

43 = 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 = 43

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\neq0,then

(p/q)3 = (p*p*p)/(q*q*q)

= p3/q3

So,

(p/q)3 = p3/q3

Example:

  • (5/4)3 = 53/43 = 125/64

 

  • (3/2)3 = 33/23 = 27/8
Some Features of Cube of Numbers

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

Example:

23 = 8

43 = 64

63 = 216

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

Example:

13 = 1

33 = 27

53 = 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

cube-root   

Example:

43 = 64

Or

\sqrt[3]{64} = 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

\sqrt[3]{-64} = -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 \frac{216}{125}

cube-root-rational

So, the cube root of \frac{216}{125} is \frac{6}{5}