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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 x3 = 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

Cube Root of 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.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 2?

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

  1. 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

  2. Example 2: Find the real root of the equation x3 − 2 = 0.

    Solution:

    x3 − 2 = 0 i.e. x3 = 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 x3 − 2 = 0 is for x = ∛2 = 1.2599.

  3. Example 3: The volume of a spherical ball is 2π in3. What is the radius of this ball?

    Solution:

    Volume of the spherical ball = 2π in3
    = 4/3 × π × R3
    ⇒ R3 = 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 in3

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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 = (21/3)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.

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