Cube Root – Definition – Examples

The Cube root of a number, is a number when multiply three times gives that number.

Symbolic form of Cube Root is  ∛ 

∛  is the radical symbol of root. The little three
represents that it is cube root.

The value of Index is 3, the Radicand is 8 and Radical 
symbol is shown in above figure.

Example- 

1.                     2 x 2 x 2 = 8

                                2³  = 8

so cubic root of 8 is 2.

we can write, ∛8 = 2 and read as, cubic root of 8 is 2.

2.                     3 x 3 x 3 = 27

                                3³  = 27

so cubic root of 27 is 3.

we can write,  ∛27 = 3 and read as ,cubic root of 27 is 3

3.                      4 x 4 x 4 = 64

                                4³  = 64

we can write, ∛64 = 4 and read as ,cubic root of 64 is 4.

4. 5 x 5 x 5 = 125

                                5^{3  = 125}
so cubic root of 125 is 5

we can write,  ∛125 = 5. 

  Cube Root of Negative Numbers

Example 1: -2 x -2 x -2 = -8

                                -2^{3  = -8}

Cubic of -2 is 8

Cubic root of -8 is

Example 2:   -3 x -3 x -3 = -27

                                -3^{3  = -27}

                        Cube of -3 is -27

Cubic root of -27 is -3

   ∛-27 = -3

Example 3:   -4 x -4 x -4 = -64

                                -4^{3  = -64}

                        Cube of -4 is -64

Cubic root of -64 is -4

                             ∛-64 = -4

Example 4: -5 x -5 x -5 = – 125

                                -5^{3  = -125}
                        Cube of -5 is -125

Cubic root of -125 is -5

∛-125 = -5. 

Cube of a positive number is always positive number.

Cube of a negative number is always negative number.

Cube of a zero is always zero.