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Cube Root of 108

The value of the cube root of 108 rounded to 6 decimal places is 4.762203. It is the real solution of the equation x³ = 108. The cube root of 108 is expressed as ∛108 or 3 ∛4 in the radical form and as (108)^⅓ or (108)^0.33 in the exponent form. The prime factorization of 108 is 2 × 2 × 3 × 3 × 3, hence, the cube root of 108 in its lowest radical form is expressed as 3 ∛4.

Cube root of 108: 4.762203156
Cube root of 108 in Exponential Form: (108)^⅓
Cube root of 108 in Radical Form: ∛108 or 3 ∛4

1.	What is the Cube Root of 108?
2.	How to Calculate the Cube Root of 108?
3.	Is the Cube Root of 108 Irrational?
4.	FAQs on Cube Root of 108

What is the Cube Root of 108?

The cube root of 108 is the number which when multiplied by itself three times gives the product as 108. Since 108 can be expressed as 2 × 2 × 3 × 3 × 3. Therefore, the cube root of 108 = ∛(2 × 2 × 3 × 3 × 3) = 4.7622.

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How to Calculate the Value of the Cube Root of 108?

Cube Root of 108 by Halley's Method

Its formula is ∛a ≈ x ((x³ + 2a)/(2x³ + a))
where,
a = number whose cube root is being calculated
x = integer guess of its cube root.

Here a = 108
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 108]
⇒ x = 4
Therefore,
∛108 = 4 (4³ + 2 × 108)/(2 × 4³ + 108)) = 4.75
⇒ ∛108 ≈ 4.75
Therefore, the cube root of 108 is 4.75 approximately.

Is the Cube Root of 108 Irrational?

Yes, because ∛108 = ∛(2 × 2 × 3 × 3 × 3) = 3 ∛4 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 108 is an irrational number.

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Cube Root of 108 Solved Examples

Example 1: What is the value of ∛108 ÷ ∛(-108)?

Solution:

The cube root of -108 is equal to the negative of the cube root of 108.
⇒ ∛-108 = -∛108

Therefore,
⇒ ∛108/∛(-108) = ∛108/(-∛108) = -1
Example 2: The volume of a spherical ball is 108π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 108π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 108
⇒ R = ∛(3/4 × 108) = ∛(3/4) × ∛108 = 0.90856 × 4.7622 (∵ ∛(3/4) = 0.90856 and ∛108 = 4.7622)
⇒ R = 4.32674 in³
Example 3: Given the volume of a cube is 108 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 108 in³ = a³
⇒ a³ = 108
Cube rooting on both sides,
⇒ a = ∛108 in
Since the cube root of 108 is 4.76, therefore, the length of the side of the cube is 4.76 in.

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FAQs on Cube Root of 108

What is the Value of the Cube Root of 108?

We can express 108 as 2 × 2 × 3 × 3 × 3 i.e. ∛108 = ∛(2 × 2 × 3 × 3 × 3) = 4.7622. Therefore, the value of the cube root of 108 is 4.7622.

Is 108 a Perfect Cube?

The number 108 on prime factorization gives 2 × 2 × 3 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 108 is irrational, hence 108 is not a perfect cube.

If the Cube Root of 108 is 4.76, Find the Value of ∛0.108.

Let us represent ∛0.108 in p/q form i.e. ∛(108/1000) = 4.76/10 = 0.48. Hence, the value of ∛0.108 = 0.48.

What is the Cube Root of -108?

The cube root of -108 is equal to the negative of the cube root of 108. Therefore, ∛-108 = -(∛108) = -(4.762) = -4.762.

How to Simplify the Cube Root of 108/729?

We know that the cube root of 108 is 4.7622 and the cube root of 729 is 9. Therefore, ∛(108/729) = (∛108)/(∛729) = 4.762/9 = 0.5291.

What is the Cube of the Cube Root of 108?

The cube of the cube root of 108 is the number 108 itself i.e. (∛108)³ = (108^1/3)³ = 108.