# FIND CUBE ROOTS OF A RATIONAL NUMBER

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

Find cube root of rational number ?

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

Step 1 :

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

Step 2 :

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

Evaluate:

Problem 1 :

∛(1/125)

Solution :

(1/125)

Distribute the cube root to numerator and denominator.

1 / 125

= (1 ∙ 1 ∙ 1) /(5 ∙ 5 ∙ 5)

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.

= 1/5

Problem 2 :

∛(-8/27)

Solution :

∛(-8/27)

Distribute the cube root to numerator and denominator.

-8 / 27

= - (2 ∙ 2 ∙ 2) / (3 ∙ 3 ∙ 3)

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.

= -2/3

Problem 3 :

343/64

Solution :

∛(343/64)

Distribute the cube root to numerator and denominator.

∛(343 / 64)

= (7 ∙ 7 ∙ 7) / (4 ∙ 4 ∙ 4)

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.

= 7/4

Problem 4 :

-1  91/125

Solution :

= -1  91/125

= -∛(216/125)

Distribute the cube root to numerator and denominator.

= -∛(216 / 125)

= -(6 ∙ 6 ∙ 6) / (5 ∙ 5 ∙ 5)

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.

= -6/5

Problem 5 :

∛(1/64)

Solution :

∛(1/64)

Distribute the cube root to numerator and denominator.

∛(1 / 64)

= (1 ∙ 1 ∙ 1) / (4 ∙ 4 ∙ 4)

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.

= 1/4

Problem 6 :

3  3/8

Solution :

3  3/8

Converting the mixed fraction into improper fraction, we get

27/8

Distribute the cube root to numerator and denominator.

27 / 8

= ∛(3 ∙ 3 ∙ 3) / ∛(2 ∙ 2 ∙ 2)

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.

= 3/2

Problem 7 :

-216

Solution :

-216

We can write 216 as 6 × 6 × 6,

-216 = ∛(- 6 × -6 × -6)

-216 = -6

Problem 8 :

27/125

Solution :

∛(27/125)

Distribute the cube root to numerator and denominator.

∛(27 / 125)

= (3 ∙ 3 ∙ 3) / (5 ∙ 5 ∙ 5)

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.

= 3/5

Problem 9 :

∛(343/1000)

Solution :

∛(343/1000)

Distribute the cube root to numerator and denominator.

= -∛(343 / 1000)

= - (7 ∙ 7 ∙ 7) / (10 ∙ 10 ∙ 10)

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.

= -7/10

Problem 10 :

729/64

Solution :

∛(729/64)

Distribute the cube root to numerator and denominator.

∛(729 / 64)

= (9 ∙ 9 ∙ 9) / (4 ∙ 4 ∙ 4)

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.

= 9/4

## Recent Articles

1. ### Finding Range of Values Inequality Problems

May 21, 24 08:51 PM

Finding Range of Values Inequality Problems

2. ### Solving Two Step Inequality Word Problems

May 21, 24 08:51 AM

Solving Two Step Inequality Word Problems