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Cube Root of 6

The value of the cube root of 6 rounded to 6 decimal places is 1.817121. It is the real solution of the equation x³ = 6. The cube root of 6 is expressed as ∛6 in the radical form and as (6)^⅓ or (6)^0.33 in the exponent form. The prime factorization of 6 is 2 × 3, hence, the cube root of 6 in its lowest radical form is expressed as ∛6.

Cube root of 6: 1.817120593
Cube root of 6 in Exponential Form: (6)^⅓
Cube root of 6 in Radical Form: ∛6

1.	What is the Cube Root of 6?
2.	How to Calculate the Cube Root of 6?
3.	Is the Cube Root of 6 Irrational?
4.	FAQs on Cube Root of 6

What is the Cube Root of 6?

The cube root of 6 is the number which when multiplied by itself three times gives the product as 6. Since 6 can be expressed as 2 × 3. Therefore, the cube root of 6 = ∛(2 × 3) = 1.8171.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 6?

Cube Root of 6 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 = 6
Let us assume x as 1
[∵ 1³ = 1 and 1 is the nearest perfect cube that is less than 6]
⇒ x = 1
Therefore,
∛6 = 1 (1³ + 2 × 6)/(2 × 1³ + 6)) = 1.62
⇒ ∛6 ≈ 1.62
Therefore, the cube root of 6 is 1.62 approximately.

Is the Cube Root of 6 Irrational?

Yes, because ∛6 = ∛(2 × 3) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 6 is an irrational number.

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Cube Root of 6 Solved Examples

Example 1: The volume of a spherical ball is 6π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 6π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 6
⇒ R = ∛(3/4 × 6) = ∛(3/4) × ∛6 = 0.90856 × 1.81712 (∵ ∛(3/4) = 0.90856 and ∛6 = 1.81712)
⇒ R = 1.65096 in³
Example 2: What is the value of ∛6 + ∛(-6)?

Solution:

The cube root of -6 is equal to the negative of the cube root of 6.
i.e. ∛-6 = -∛6

Therefore, ∛6 + ∛(-6) = ∛6 - ∛6 = 0
Example 3: Find the real root of the equation x³ − 6 = 0.

Solution:

x³ − 6 = 0 i.e. x³ = 6
Solving for x gives us,
x = ∛6, x = ∛6 × (-1 + √3i))/2 and x = ∛6 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛6
Therefore, the real root of the equation x³ − 6 = 0 is for x = ∛6 = 1.8171.

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FAQs on Cube Root of 6

What is the Value of the Cube Root of 6?

We can express 6 as 2 × 3 i.e. ∛6 = ∛(2 × 3) = 1.81712. Therefore, the value of the cube root of 6 is 1.81712.

Is 6 a Perfect Cube?

The number 6 on prime factorization gives 2 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 6 is irrational, hence 6 is not a perfect cube.

If the Cube Root of 6 is 1.82, Find the Value of ∛0.006.

Let us represent ∛0.006 in p/q form i.e. ∛(6/1000) = 1.82/10 = 0.18. Hence, the value of ∛0.006 = 0.18.

How to Simplify the Cube Root of 6/125?

We know that the cube root of 6 is 1.81712 and the cube root of 125 is 5. Therefore, ∛(6/125) = (∛6)/(∛125) = 1.817/5 = 0.3634.

What is the Cube Root of -6?

The cube root of -6 is equal to the negative of the cube root of 6. Therefore, ∛-6 = -(∛6) = -(1.817) = -1.817.

What is the Cube of the Cube Root of 6?

The cube of the cube root of 6 is the number 6 itself i.e. (∛6)³ = (6^1/3)³ = 6.