CUBE ROOT OF THE GIVEN NUMBER

Cube root of a number is the factor that we multiply by itself three times to get that number. The symbol

To find a cube root of a number, we will follow the steps.

Step 1 :

Decompose the numerators and denominator separately as product of prime factors.

Step 2 :

For every three same value, we can take one out of the radical.

Finding cube root of rational number ?

Using the following property, we find cube root of rational number.

Cube root of negative numbers :

Cube root of negative number is also negative.

For example,

Evaluate each of the following:

Problem 1 :

-27

Solution :

= -27

We can write 27 as 3 × 3 × 3,

-27 = - (3 × 3 × 3)

-27 = -3

Problem 2 :

1/8

Solution :

= 1/8

= 1/ 8

= 1/2

Problem 3 :

27

Solution :

= 27

We can write 27 as 3 × 3 × 3,

27 = (3 × 3 × 3)

27 = 3

Problem 4 :

- ∛1/64

Solution :

= -1/64

= -1/ 64

= -1/4

Problem 5 :

∛-8/27

Solution :

= ∛-8/27

= -8/ 27

= -2/3

Problem 6 :

-1000

Solution :

= -1000

We can write 1000 as 10 × 10 × 10,

-1000 = -(10 × 10 × 10)

-1000 = -10

Problem 7 :

∛-27/64

Solution :

= ∛-27/64

= -27/ 64

= -3/4

Problem 8:

-∛-64

Solution :

= --64

We can write 64 as 4 × 4 × 4,

-∛-64 = -∛ -(4 × 4 × 4)

-∛-64 = 4

Problem 9 :

∛-1/125

Solution :

= ∛-1/125

= ∛-1/ 125

= -1/5

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