Cube Root of 2
The value of the cube root of 2 rounded to 6 decimal places is 1.259921. It is the real solution of the equation x^{3} = 2. The cube root of 2 is expressed as ∛2 in the radical form and as (2)^{⅓} or (2)^{0.33} in the exponent form. The prime factorization of 2 is 2, hence, the cube root of 2 in its lowest radical form is expressed as ∛2.
 Cube root of 2: 1.25992105
 Cube root of 2 in Exponential Form: (2)^{⅓}
 Cube root of 2 in Radical Form: ∛2
1.  What is the Cube Root of 2? 
2.  How to Calculate the Cube Root of 2? 
3.  Is the Cube Root of 2 Irrational? 
4.  FAQs on Cube Root of 2 
What is the Cube Root of 2?
The cube root of 2 is the number which when multiplied by itself three times gives the product as 2. The number 2 is prime. Therefore, the cube root of 2 = ∛2 = 1.2599.
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How to Calculate the Value of the Cube Root of 2?
Cube Root of 2 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 = 2
Let us assume x as 1
[∵ 1^{3} = 1 and 1 is the nearest perfect cube that is less than 2]
⇒ x = 1
Therefore,
∛2 = 1 (1^{3} + 2 × 2)/(2 × 1^{3} + 2)) = 1.25
⇒ ∛2 ≈ 1.25
Therefore, the cube root of 2 is 1.25 approximately.
Is the Cube Root of 2 Irrational?
Yes, because ∛2 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 2 is an irrational number.
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Cube Root of 2 Solved Examples

Example 1: What is the value of ∛2 + ∛(2)?
Solution:
The cube root of 2 is equal to the negative of the cube root of 2.
i.e. ∛2 = ∛2
Therefore, ∛2 + ∛(2) = ∛2  ∛2 = 0

Example 2: Find the real root of the equation x^{3} − 2 = 0.
Solution:
x^{3} − 2 = 0 i.e. x^{3} = 2
Solving for x gives us,
x = ∛2, x = ∛2 × (1 + √3i))/2 and x = ∛2 × (1  √3i))/2
where i is called the imaginary unit and is equal to √1.
Ignoring imaginary roots,
x = ∛2
Therefore, the real root of the equation x^{3} − 2 = 0 is for x = ∛2 = 1.2599.

Example 3: The volume of a spherical ball is 2π in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 2π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 3/4 × 2
⇒ R = ∛(3/4 × 2) = ∛(3/4) × ∛2 = 0.90856 × 1.25992 (∵ ∛(3/4) = 0.90856 and ∛2 = 1.25992)
⇒ R = 1.14471 in^{3}
FAQs on Cube Root of 2
What is the Value of the Cube Root of 2?
The value of the cube root of 2 is 1.25992.
What is the Cube of the Cube Root of 2?
The cube of the cube root of 2 is the number 2 itself i.e. (∛2)^{3} = (2^{1/3})^{3} = 2.
Is 2 a Perfect Cube?
The number 2 is prime. Here, the prime factor 2 is not in the power of 3 and this implies that the cube root of 2 is irrational, hence 2 is not a perfect cube.
What is the Value of 18 Plus 5 Cube Root 2?
The value of ∛2 is 1.26. So, 18 + 5 × ∛2 = 18 + 5 × 1.26 = 24.3. Hence, the value of 18 plus 5 cube root 2 is 24.3.
If the Cube Root of 2 is 1.26, Find the Value of ∛0.002.
Let us represent ∛0.002 in p/q form i.e. ∛(2/1000) = 1.26/10 = 0.13. Hence, the value of ∛0.002 = 0.13.
Why is the Value of the Cube Root of 2 Irrational?
The value of the cube root of 2 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛2 is irrational.