A cube has three-dimensional solid shape and bounded by six square faces, facets or sides, with three meeting at each vertex.
Numbers obtained when a number is multiplied by itself three times are known as cube numbers.
For example 1, 8, 27, ... etc.
The word cube is used in geometry. In term of number cube just use in a multiplication 3 times.
|
Number |
Cube |
|
1 |
13 = 1 |
|
2 |
23 = 8 |
|
3 |
33 = 9 |
|
4 |
43 = 64 |
|
5 |
53 = 125 |
|
6 |
63 = 216 |
|
7 |
73 = 343 |
|
8 |
83 = 512 |
|
9 |
93 = 729 |
|
10 |
103 = 1000 |
These are called perfect cubes or cube numbers.
Also there are various patterns to find the cube of the number-
Observe the following pattern of sums of odd numbers.
1 = 1 = 13
3 + 5 = 8 = 23
7 + 9 + 11 = 27 = 33
13 + 15 + 17 + 19 = 64 = 43
21 + 23 + 25 + 27 + 29 = 125 = 53
Finding the cube root is the inverse operation of finding cube.
The symbol ∛ denotes ‘cube-root.’
Consider the following -:
|
Statements |
Inference |
|
13 =1 |
∛1 = 1 |
|
23 = 8 |
∛8 = 2 |
|
33 = 9 |
∛9 = 3 |
Also there are various patterns to find the cube root of the number-
Consider 3375. We find its cube root by prime factorisation:
3375 = 3 x 3 x 3 x 5 x 5 x 5 = 33 x 53 = (3 x 5)3
Therefore, cube root of ∛3375 = 3 x 5 = 15