- 1) What is a cube in Math?
- 2) What is Cube Root?
- 3) Cube Root of a negative number:
- 4) Cube Root of a Rational Number:
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.
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
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.
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.
- (-3)3 = (-3)*(-3)*(-3) = -27
- (-4)3 = (-4)*(-4)*(-4) = -64
Cube of Rational Numbers
We have a rational number p/q and q0,then
(p/q)3 = (p*p*p)/(q*q*q)
(p/q)3 = p3/q3
- (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.
23 = 8
43 = 64
63 = 216
The resultant of the cube of Odd Natural numbers is also an odd number.
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
43 = 64
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:
-64 = (-4)3
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.
Cube Root of
So, the cube root of is