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Cube Root of 12

The value of the cube root of 12 rounded to 6 decimal places is 2.289428. It is the real solution of the equation x3 = 12. The cube root of 12 is expressed as ∛12 in the radical form and as (12)⅓ or (12)0.33 in the exponent form. The prime factorization of 12 is 2 × 2 × 3, hence, the cube root of 12 in its lowest radical form is expressed as ∛12.

  • Cube root of 12: 2.289428485
  • Cube root of 12 in Exponential Form: (12)⅓
  • Cube root of 12 in Radical Form: ∛12

Cube Root of 12

1. What is the Cube Root of 12?
2. How to Calculate the Cube Root of 12?
3. Is the Cube Root of 12 Irrational?
4. FAQs on Cube Root of 12

What is the Cube Root of 12?

The cube root of 12 is the number which when multiplied by itself three times gives the product as 12. Since 12 can be expressed as 2 × 2 × 3. Therefore, the cube root of 12 = ∛(2 × 2 × 3) = 2.2894.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 12?

Cube Root of 12 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 = 12
Let us assume x as 2
[∵ 23 = 8 and 8 is the nearest perfect cube that is less than 12]
⇒ x = 2
Therefore,
∛12 = 2 (23 + 2 × 12)/(2 × 23 + 12)) = 2.29
⇒ ∛12 ≈ 2.29
Therefore, the cube root of 12 is 2.29 approximately.

Is the Cube Root of 12 Irrational?

Yes, because ∛12 = ∛(2 × 2 × 3) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 12 is an irrational number.

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Cube Root of 12 Solved Examples

  1. Example 1: Find the real root of the equation x3 − 12 = 0.

    Solution:

    x3 − 12 = 0 i.e. x3 = 12
    Solving for x gives us,
    x = ∛12, x = ∛12 × (-1 + √3i))/2 and x = ∛12 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛12
    Therefore, the real root of the equation x3 − 12 = 0 is for x = ∛12 = 2.2894.

  2. Example 2: What is the value of ∛12 ÷ ∛(-12)?

    Solution:

    The cube root of -12 is equal to the negative of the cube root of 12.
    ⇒ ∛-12 = -∛12

    Therefore,
    ⇒ ∛12/∛(-12) = ∛12/(-∛12) = -1

  3. Example 3: The volume of a spherical ball is 12π in3. What is the radius of this ball?

    Solution:

    Volume of the spherical ball = 12π in3
    = 4/3 × π × R3
    ⇒ R3 = 3/4 × 12
    ⇒ R = ∛(3/4 × 12) = ∛(3/4) × ∛12 = 0.90856 × 2.28943 (∵ ∛(3/4) = 0.90856 and ∛12 = 2.28943)
    ⇒ R = 2.08008 in3

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FAQs on Cube Root of 12

What is the Value of the Cube Root of 12?

We can express 12 as 2 × 2 × 3 i.e. ∛12 = ∛(2 × 2 × 3) = 2.28943. Therefore, the value of the cube root of 12 is 2.28943.

Why is the Value of the Cube Root of 12 Irrational?

The value of the cube root of 12 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛12 is irrational.

What is the Value of 1 Plus 4 Cube Root 12?

The value of ∛12 is 2.289. So, 1 + 4 × ∛12 = 1 + 4 × 2.289 = 10.156. Hence, the value of 1 plus 4 cube root 12 is 10.156.

How to Simplify the Cube Root of 12/8?

We know that the cube root of 12 is 2.28943 and the cube root of 8 is 2. Therefore, ∛(12/8) = (∛12)/(∛8) = 2.289/2 = 1.1445.

What is the Cube of the Cube Root of 12?

The cube of the cube root of 12 is the number 12 itself i.e. (∛12)3 = (121/3)3 = 12.

If the Cube Root of 12 is 2.29, Find the Value of ∛0.012.

Let us represent ∛0.012 in p/q form i.e. ∛(12/1000) = 2.29/10 = 0.23. Hence, the value of ∛0.012 = 0.23.

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