The worth of the cube source of 108 rounded to 6 decimal places is 4.762203. The is the genuine solution of the equation x3 = 108. The cube root of 108 is expressed together ∛108 or 3 ∛4 in the radical type and as (108)⅓ or (108)0.33 in the exponent form. The element factorization the 108 is 2 × 2 × 3 × 3 × 3, hence, the cube root of 108 in its lowest radical type is expressed as 3 ∛4.

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Cube root of 108: 4.762203156 Cube source of 108 in Exponential Form: (108)⅓Cube source of 108 in Radical Form: ∛108 or 3 ∛4
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1.What is the Cube root of 108?
2.How to calculate the Cube source of 108?
3.Is the Cube source of 108 Irrational?
4.FAQs ~ above Cube source of 108

What is the Cube source of 108?


The cube root of 108 is the number which when multiplied by itself three times provides the product together 108. Since 108 deserve to be expressed together 2 × 2 × 3 × 3 × 3. Therefore, the cube source of 108 = ∛(2 × 2 × 3 × 3 × 3) = 4.7622.

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exactly how to calculate the value of the Cube root of 108?


Cube source of 108 through Halley"s technique

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

right 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 source of 108 is 4.75 approximately.


Is the Cube source of 108 Irrational?


Yes, due to the fact that ∛108 = ∛(2 × 2 × 3 × 3 × 3) = 3 ∛4 and also it cannot be to express in the form of p/q whereby q ≠ 0. Therefore, the value of the cube root of 108 is one irrational number.

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Cube root of 108 solved Examples


example 1: What is the worth of ∛108 ÷ ∛(-108)?

Solution:

The cube root of -108 is same to the an unfavorable of the cube root of 108. ⇒ ∛-108 = -∛108 Therefore, ⇒ ∛108/∛(-108) = ∛108/(-∛108) = -1


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FAQs top top Cube root of 108

What is the value of the Cube root of 108?

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

Is 108 a Perfect Cube?

The number 108 on prime factorization offers 2 × 2 × 3 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Thus the cube root of 108 is irrational, therefore 108 is no a perfect cube.

If the Cube source of 108 is 4.76, find the value of ∛0.108.

Let us represent ∛0.108 in p/q kind 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 same to the negative of the cube root of 108. Therefore, ∛-108 = -(∛108) = -(4.762) = -4.762.

How to leveling the Cube source of 108/729?

We understand 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.

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What is the Cube the the Cube root of 108?

The cube of the cube root of 108 is the number 108 itself i.e. (∛108)3 = (1081/3)3 = 108.