# Cubes And Cube Roots

Cube is a geometrical shape. It is a three dimensional solid figure and it’s all sides are equal.
How many cubes of sides 1 cm make a cube of side 2cm, 3cm, 4cm etc?
With 1 cm side we get 1 cube, with 2 cm side we get 8 cubes each of 1 cm, with 3 cm side we get 27 cubes each of 1 cm and so on.
The numbers 1, 8, 27, 64 etc are called perfect cubes or cube numbers. We get each number when a number is multiplied by itself three times.
Therefore, cube numbers can be defined as when a number is multiplied by itself three times then the number obtained are known as a cube numbers. For example:
Cube of 1= 1, 23 =   8,  33 =  27 , 43 = 64 etc.
If a natural number ‘m’ can be expressed as n3, where ‘n’ is also a natural number and ‘m’ is a cube number or perfect cube.
Now consider that volume of cube is 216 cm3, and then what would be the length of its side?
Therefore, to find out the side, we need a number whose cube is 216. For this we have to calculate a cube root.
Finding cube and cube roots is the inverse process.
The symbol which denotes the cube root is ∛x.
For example, ∛216 = 2 x 2  x 2 x 3 x 3 x 3  =  23  x  33
Therefore,  ∛216   =  2 x 3 = 6

In the prime factorization of any number, if each factor appears 3 times, then it is a perfect cube and cube roots of a number can be finding out by using prime factorization method.
Firstly, find the prime factor of a given number.
Then make a group of three same numbers and finally take a common number from each group and then we get the cube.
Suppose we have to find out the cube root of 512, the prime factor of 512 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.
Make a group of three as 23 x 23 x 23.
Finally take the common number as 2 x 2 x 2 = 8
Therefore, ∛512 = 8.

This is all about cubes and cube roots.

Math Topics