Theory:

The inverse operation of a cube is cube root. The symbol used to represent the cube root is \(\sqrt[3]{}\).
 
A cube root is a unique value that gives us the original number when we multiply itself by three times.
 
The cube root of \(a\) is denoted by \(\sqrt[3]{a}\) or \(a^{\frac{1}{3}}\).
Example:
Find the cube root of \(64\).
 
Solution:
 
\(\sqrt[3]{64} = \sqrt[3]{4 \times 4 \times 4}\) \(= \sqrt[3]{4^3}\) \( = 4\)
 
Thereforethe cube root of \(64\) is \(4\).
By the observation of the above example, we can conclude that:
 
The cube of \(4\) is \(64\).
 
The cube root of \(64\) is \(4\).
 
cube_4_64 (1).png
 
The following table consist of cube and cube roots of the first \(20\) numbers.
 
Number
Cube number
Cube root
Number
Cube number
Cube root
1
\(1^3 = 1\)
\(\sqrt[3]{1} = 1\)
11
\(11^3 = 1331\)
\(\sqrt[3]{1331} = 11\)
2
\(2^3 = 8\)
\(\sqrt[3]{8} = 2\)
12
\(12^3 = 1728\)
\(\sqrt[3]{1728} = 12\)
3
\(3^3 = 27\)
\(\sqrt[3]{27} = 3\)
13
\(13^3 = 2197\)
\(\sqrt[3]{2197} = 13\)
4
\(4^3 = 64\)
\(\sqrt[3]{64} = 4\)
14
\(14^3 = 2744\)
\(\sqrt[3]{2744} = 14\)
5
\(5^3 = 125\)
\(\sqrt[3]{125} = 5\)
15
\(15^3 = 3375\)
\(\sqrt[3]{3375} = 15\)
6
\(6^3 = 216\)
\(\sqrt[3]{216} = 6\)
16
\(16^3 = 4096\)
\(\sqrt[3]{4096} = 16\)
7
\(7^3 = 343\)
\(\sqrt[3]{343} = 7\)
17
\(17^3 = 4913\)
\(\sqrt[3]{4913} = 17\)
8
\(8^3 = 512\)
\(\sqrt[3]{512} = 8\)
18
\(18^3 = 5832\)
\(\sqrt[3]{5832} = 18\)
9
\(9^3 = 729\)
\(\sqrt[3]{729} = 9\)
19
\(19^3 = 6859\)
\(\sqrt[3]{6859} = 19\)
10
\(10^3 = 1000\)
\(\sqrt[3]{1000} = 10\)
20
\(20^3 = 8000\)
\(\sqrt[3]{8000} = 20\)