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 x^{3} = 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 ((x^{3} + 2a)/(2x^{3} + 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
[∵ 1^{3} = 1 and 1 is the nearest perfect cube that is less than 6]
⇒ x = 1
Therefore,
∛6 = 1 (1^{3} + 2 × 6)/(2 × 1^{3} + 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.
☛ Also Check:
 Cube Root of 294
 Cube Root of 625
 Cube Root of 88
 Cube Root of 100
 Cube Root of 81
 Cube Root of 2304
 Cube Root of 80
Cube Root of 6 Solved Examples

Example 1: The volume of a spherical ball is 6π in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 6π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 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 in^{3} 
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 x^{3} − 6 = 0.
Solution:
x^{3} − 6 = 0 i.e. x^{3} = 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 x^{3} − 6 = 0 is for x = ∛6 = 1.8171.
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.
visual curriculum