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Cube Root of 2000

The value of the cube root of 2000 rounded to 6 decimal places is 12.59921. It is the real solution of the equation x3 = 2000. The cube root of 2000 is expressed as ∛2000 or 10 ∛2 in the radical form and as (2000)⅓ or (2000)0.33 in the exponent form. The prime factorization of 2000 is 2 × 2 × 2 × 2 × 5 × 5 × 5, hence, the cube root of 2000 in its lowest radical form is expressed as 10 ∛2.

  • Cube root of 2000: 12.599210499
  • Cube root of 2000 in Exponential Form: (2000)⅓
  • Cube root of 2000 in Radical Form: ∛2000 or 10 ∛2

Cube Root of 2000

1. What is the Cube Root of 2000?
2. How to Calculate the Cube Root of 2000?
3. Is the Cube Root of 2000 Irrational?
4. FAQs on Cube Root of 2000

What is the Cube Root of 2000?

The cube root of 2000 is the number which when multiplied by itself three times gives the product as 2000. Since 2000 can be expressed as 2 × 2 × 2 × 2 × 5 × 5 × 5. Therefore, the cube root of 2000 = ∛(2 × 2 × 2 × 2 × 5 × 5 × 5) = 12.5992.

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How to Calculate the Value of the Cube Root of 2000?

Cube Root of 2000 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 = 2000
Let us assume x as 12
[∵ 123 = 1728 and 1728 is the nearest perfect cube that is less than 2000]
⇒ x = 12
Therefore,
∛2000 = 12 (123 + 2 × 2000)/(2 × 123 + 2000)) = 12.6
⇒ ∛2000 ≈ 12.6
Therefore, the cube root of 2000 is 12.6 approximately.

Is the Cube Root of 2000 Irrational?

Yes, because ∛2000 = ∛(2 × 2 × 2 × 2 × 5 × 5 × 5) = 10 ∛2 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 2000 is an irrational number.

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Cube Root of 2000 Solved Examples

  1. Example 1: Given the volume of a cube is 2000 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 2000 in3 = a3
    ⇒ a3 = 2000
    Cube rooting on both sides,
    ⇒ a = ∛2000 in
    Since the cube root of 2000 is 12.6, therefore, the length of the side of the cube is 12.6 in.

  2. Example 2: Find the real root of the equation x3 − 2000 = 0.

    Solution:

    x3 − 2000 = 0 i.e. x3 = 2000
    Solving for x gives us,
    x = ∛2000, x = ∛2000 × (-1 + √3i))/2 and x = ∛2000 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛2000
    Therefore, the real root of the equation x3 − 2000 = 0 is for x = ∛2000 = 12.5992.

  3. Example 3: What is the value of ∛2000 + ∛(-2000)?

    Solution:

    The cube root of -2000 is equal to the negative of the cube root of 2000.
    i.e. ∛-2000 = -∛2000

    Therefore, ∛2000 + ∛(-2000) = ∛2000 - ∛2000 = 0

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FAQs on Cube Root of 2000

What is the Value of the Cube Root of 2000?

We can express 2000 as 2 × 2 × 2 × 2 × 5 × 5 × 5 i.e. ∛2000 = ∛(2 × 2 × 2 × 2 × 5 × 5 × 5) = 12.59921. Therefore, the value of the cube root of 2000 is 12.59921.

How to Simplify the Cube Root of 2000/216?

We know that the cube root of 2000 is 12.59921 and the cube root of 216 is 6. Therefore, ∛(2000/216) = (∛2000)/(∛216) = 12.599/6 = 2.0998.

What is the Value of 6 Plus 6 Cube Root 2000?

The value of ∛2000 is 12.599. So, 6 + 6 × ∛2000 = 6 + 6 × 12.599 = 81.594. Hence, the value of 6 plus 6 cube root 2000 is 81.594.

What is the Cube of the Cube Root of 2000?

The cube of the cube root of 2000 is the number 2000 itself i.e. (∛2000)3 = (20001/3)3 = 2000.

What is the Cube Root of -2000?

The cube root of -2000 is equal to the negative of the cube root of 2000. Therefore, ∛-2000 = -(∛2000) = -(12.599) = -12.599.

Is 2000 a Perfect Cube?

The number 2000 on prime factorization gives 2 × 2 × 2 × 2 × 5 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 2000 is irrational, hence 2000 is not a perfect cube.

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