Cube Root of a number can be obtained by doing the inverse operation of calculating cube. In general terms, the cube root of a number is identified by a number that multiplied by itself thrice gives you the cube root of that number. The cube root of any number is denoted with the symbol ∛. Look at the **Cube and Cube Roots** solved examples and their explanations to learn them easily.

For example, the cube root of a number x is represented as ∛x.

## How to Find the Cube Root of a Number?

Simply, Note down the product of primes a number. Then, form the groups in triplets using the product of primes a number. After that take one number from each triplet. The selected single number is the required cube root of the given number.

**Note:** If you find a group of prime factors that cannot form a group in triplets they remain the same and their cube root cannot be found.

### Cube Root of a Number Solved Examples

**(i) Find the Cube Root of a number 64?**

**Answer:**

Write the product of primes of a given number 64 those form groups in triplets.

Cube Root of 64 = ∛64 = ∛(4 × 4 × 4)

Take one number from a group of triplets to find the cube root of 64.

Therefore, 4 is the cube root of a given number 64.

4 is the cube root of a given number 64.

**(ii) Find the Cube Root of a number 8?**

**Answer:**

Write the product of primes of a given number 8 those form groups in triplets.

Cube Root of 8= ∛8= ∛(2 × 2 × 2)

Take one number from a group of triplets to find the cube root of 8.

Therefore, 2 is the cube root of a given number 8.

2 is the cube root of a given number 8.

**(iii) Find the Cube Root of a number 125?**

**Answer:**

Write the product of primes of a given number 125 those form groups in triplets.

Cube Root of 125= ∛125= ∛(5 × 5 × 5)

Take one number from a group of triplets to find the cube root of 125.

Therefore, 5 is the cube root of a given number 125.

5 is the cube root of a given number 125.

**(iv) Find the Cube Root of a number 27?**

**Answer:**

Write the product of primes of a given number 27 those form groups in triplets.

Cube Root of 27 = ∛27 = ∛(3 × 3 × 3)

Take one number from a group of triplets to find the cube root of 27.

Therefore, 3 is the cube root of a given number 27.

3 is the cube root of a given number 27.

**(iv) Find the Cube Root of a number 216?**

**Answer:**

Write the product of primes of a given number 216 those form groups in triplets.

Cube Root of 216 = ∛216 = ∛(6 × 6 × 6)

Take one number from a group of triplets to find the cube root of 216.

Therefore, 6 is the cube root of a given number 216.

6 is the cube root of a given number 216.

### Finding Cube Root by Prime Factorisation Method

Find the cube root of a number using the Prime Factorisation Method with the help of the below steps.

Step 1: Firstly, take the given number.

Step 2: Find the prime factors of the given number.

Step 3: Group the prime factors into each triplet.

Step 4: Collect each one factor from each group.

Step 5: Finally, find the product of each one factor from each group.

Step 6: The resultant is the cube root of a given number.

#### Cube Root of a Number by Prime Factorisation Method Solved Examples

**(i) Find the Cube Root of 216 by Prime Factorisation Method?**

**Answer:**

Firstly, find the prime factors of the given number.

216 = 2 × 2 × 2 × 3 × 3 × 3

Group the prime factors into each triplet.

216 = (2 × 2 × 2) × (3 × 3 × 3)

Collect each one factor from each group.

2 and 3

Finally, find the product of each one factor from each group.

∛216 = 2 × 3 = 6

6 is the cube root of 216.

**(ii) Find the Cube Root of 343 by Prime Factorisation Method?**

**Answer: **

Firstly, find the prime factors of the given number.

343 = 7 × 7 × 7

Group the prime factors into each triplet.

343 = (7 × 7 × 7)

Collect each one factor from each group.

7

Finally, find the product of each one factor from each group.

∛343 = 7

7 is the cube root of 343.

**(iii) Find the Cube Root of 2744 by Prime Factorisation Method?**

**Answer:**

Firstly, find the prime factors of the given number.

2744 = 2 × 2 × 2 × 7 × 7 × 7

Group the prime factors into each triplet.

2744 = (2 × 2 × 2) × (7 × 7 × 7).

Collect each one factor from each group.

2 and 7

Finally, find the product of each one factor from each group.

∛2744 = 2 × 7 = 14

14 is the cube root of 2744.

### Cube Roots of Negative Numbers

Cube Root of a negative number is always negative. If -m be a negative number. Then, (-m)³ = -m³.

Therefore, ∛-m³ = -m.

cube root of (-m³) = -(cube root of m³).

∛-m = – ∛m

#### Solved Examples of Cube Root of a Negative Numbers

**(i) Find the Cube Root of (-1000)**

**Answer:**

Firstly, find the prime factors of the number 1000.

1000 = 2 × 2 × 2 × 5 × 5 × 5

Group the prime factors into each triplet.

1000 = (2 × 2 × 2) × (5 × 5 × 5).

Collect each one factor from each group.

2 and 5

Finally, find the product of each one factor from each group.

∛1000 = 2 × 5 = 10

∛-m = – ∛m

∛-1000 = – ∛1000 = -10

-10 is the cube root of (-1000).

(ii) Find the Cube Root of (-216)

**Answer:**

Firstly, find the prime factors of the number 216.

216 = 2 × 2 × 2 × 3 × 3 × 3

Group the prime factors into each triplet.

216 = (2 × 2 × 2) × (3 × 3 × 3)

Collect each one factor from each group.

2 and 3

Finally, find the product of each one factor from each group.

∛216 = 2 × 3 = 6

∛-216 = – ∛216

∛-216= – ∛216= -6

-6 is the cube root of -216.

### How to Find Cube Root of Product of Integers?

Cube Root of Product of Integers can be solved by using ∛ab = (∛a × ∛b)

#### Solved Examples:

**(i) Find ∛(125 × 64)?**

**Answer:**

Firstly, apply the cube root to both integers.

∛ab = (∛a × ∛b)

∛(125 × 64) = ∛125 × ∛64

Then, find the prime factors for each integer separately.

[∛{5 × 5 × 5}] × [∛{4 × 4 × 4}]

Take each integer from the group in triplets and multiply them to get the cube root of a given number.

(5 × 4) = 20

20 is the cube root of ∛(125 × 64).

**(ii) Find ∛(27 × 64)?**

**Answer:**

Firstly, apply the cube root to both integers.

∛ab = (∛a × ∛b)

∛(27 × 64) = ∛27 × ∛64

Then, find the prime factors for each integer separately.

[∛{3 × 3 × 3}] × [∛{4 × 4 × 4}]

Take each integer from the group in triplets and multiply them to get the cube root of a given number.

(3 × 4) = 12

12 is the cube root of ∛(27 × 64).

**(iii) Find ∛[216 × (-343)]?**

**Answer:**

Firstly, apply the cube root to both integers.

∛ab = (∛a × ∛b)

∛[216 × (-343)] = ∛216 × ∛-343

Then, find the prime factors for each integer separately.

[∛{6 × 6 × 6}] × [∛{(-7) × (-7) × (-7)}]

Take each integer from the group in triplets and multiply them to get the cube root of a given number.

[6 × (-7)] = -42

-42 is the cube root of ∛[216 × (-343)].

### Cube Root of a Rational Number

The Cube Root of a Rational Number can be calculated with the help of ∛(a/b) = (∛a)/(∛b). Apply the Cube Root separately to each integer available on the numerator and the denominator to find the cube root of a rational number.

#### Solved Examples of Cube Root of a Rational Number

**(i) Find ∛(216/2197)**

**Answer:**

Firstly, apply the cube root to both integers.

∛(a/b) = (∛a)/(∛b)

∛(216/2197) = ∛216/∛2197

Then, find the prime factors for each integer separately.

[∛(6 × 6 × 6)]/[ ∛(13 × 13 × 13)]

Take each integer from the group in triplets to get the cube root of a given number.

6/13

6/13 is the cube root of ∛(216/2197).

**(ii) Find ∛(27/8)**

**Answer:**

Firstly, apply the cube root to both integers.

∛(a/b) = (∛a)/(∛b)

∛(27/8) = ∛27/∛8.

Then, find the prime factors for each integer separately.

[∛(3 × 3 × 3)]/[ ∛(2 × 2 × 2)]

Take each integer from the group in triplets to get the cube root of a given number.

3/2

3/2 is the cube root of ∛(27/8).

### How to Find the Cube Root of Decimals?

The Cube Root of Decimals can easily be solved by converting them into fractions. After converting the decimal number into a fraction apply the cube root to the numerator and denominator separately. Then, convert the resultant value to decimal.

#### Cube Root of Decimals Solved Examples

**(i) Find the cube root of 5.832.**

**Answer:**

Conver the given decimal 5.832 into a fraction.

5.832 = 5832/1000

Now, apply the cube root to the fraction.

∛5832/1000

Apply the cube root to both integers.

∛(a/b) = (∛a)/(∛b)

∛5832/1000 = ∛5832/∛1000.

Then, find the prime factors for each integer separately.

∛(2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3)/∛(2 × 2 × 2 × 5 × 5 × 5)

Take each integer from the group in triplets to get the cube root of a given number.

(2 × 3 × 3)/(2 × 5) = 18/10

Convert the fraction into a decimal

18/10 = 1.8

1.8 is the cube root of 5.832.