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

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

What is the Cube source of 108?


The cube source of 108 is the number which when multiplied by itself 3 times gives the product together 108. Due to the fact that 108 can 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 an approach

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

right here a = 108 Let united state assume x as 4 <∵ 43 = 64 and also 64 is the nearest perfect cube that is much 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, because ∛108 = ∛(2 × 2 × 3 × 3 × 3) = 3 ∛4 and it can not be expressed in the kind of p/q whereby q ≠ 0. Therefore, the value of the cube source 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 equal to the an unfavorable of the cube source of 108. ⇒ ∛-108 = -∛108 Therefore, ⇒ ∛108/∛(-108) = ∛108/(-∛108) = -1


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FAQs on Cube source of 108

What is the value of the Cube source of 108?

We have the right to 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 gives 2 × 2 × 3 × 3 × 3. Here, the prime element 2 is not in the strength of 3. Thus the cube root of 108 is irrational, for this reason 108 is no a perfect cube.

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

Let us stand for ∛0.108 in p/q kind i.e. ∛(108/1000) = 4.76/10 = 0.48. Hence, the worth of ∛0.108 = 0.48.

What is the Cube source of -108?

The cube source of -108 is equal to the an adverse of the cube source of 108. Therefore, ∛-108 = -(∛108) = -(4.762) = -4.762.

How to simplify the Cube source of 108/729?

We understand that the cube source of 108 is 4.7622 and also 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 chin i.e. (∛108)3 = (1081/3)3 = 108.