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Cube Root of 3000

The value of the cube root of 3000 rounded to 7 decimal places is 14.4224957. It is the real solution of the equation x3 = 3000. The cube root of 3000 is expressed as ∛3000 or 10 ∛3 in the radical form and as (3000)⅓ or (3000)0.33 in the exponent form. The prime factorization of 3000 is 2 × 2 × 2 × 3 × 5 × 5 × 5, hence, the cube root of 3000 in its lowest radical form is expressed as 10 ∛3.

  • Cube root of 3000: 14.422495703
  • Cube root of 3000 in Exponential Form: (3000)⅓
  • Cube root of 3000 in Radical Form: ∛3000 or 10 ∛3

Cube Root of 3000

1. What is the Cube Root of 3000?
2. How to Calculate the Cube Root of 3000?
3. Is the Cube Root of 3000 Irrational?
4. FAQs on Cube Root of 3000

What is the Cube Root of 3000?

The cube root of 3000 is the number which when multiplied by itself three times gives the product as 3000. Since 3000 can be expressed as 2 × 2 × 2 × 3 × 5 × 5 × 5. Therefore, the cube root of 3000 = ∛(2 × 2 × 2 × 3 × 5 × 5 × 5) = 14.4225.

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How to Calculate the Value of the Cube Root of 3000?

Cube Root of 3000 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 = 3000
Let us assume x as 14
[∵ 143 = 2744 and 2744 is the nearest perfect cube that is less than 3000]
⇒ x = 14
Therefore,
∛3000 = 14 (143 + 2 × 3000)/(2 × 143 + 3000)) = 14.42
⇒ ∛3000 ≈ 14.42
Therefore, the cube root of 3000 is 14.42 approximately.

Is the Cube Root of 3000 Irrational?

Yes, because ∛3000 = ∛(2 × 2 × 2 × 3 × 5 × 5 × 5) = 10 ∛3 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 3000 is an irrational number.

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Cube Root of 3000 Solved Examples

  1. Example 1: Given the volume of a cube is 3000 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 3000 in3 = a3
    ⇒ a3 = 3000
    Cube rooting on both sides,
    ⇒ a = ∛3000 in
    Since the cube root of 3000 is 14.42, therefore, the length of the side of the cube is 14.42 in.

  2. Example 2: What is the value of ∛3000 ÷ ∛(-3000)?

    Solution:

    The cube root of -3000 is equal to the negative of the cube root of 3000.
    ⇒ ∛-3000 = -∛3000

    Therefore,
    ⇒ ∛3000/∛(-3000) = ∛3000/(-∛3000) = -1

  3. Example 3: Find the real root of the equation x3 − 3000 = 0.

    Solution:

    x3 − 3000 = 0 i.e. x3 = 3000
    Solving for x gives us,
    x = ∛3000, x = ∛3000 × (-1 + √3i))/2 and x = ∛3000 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛3000
    Therefore, the real root of the equation x3 − 3000 = 0 is for x = ∛3000 = 14.4225.

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FAQs on Cube Root of 3000

What is the Value of the Cube Root of 3000?

We can express 3000 as 2 × 2 × 2 × 3 × 5 × 5 × 5 i.e. ∛3000 = ∛(2 × 2 × 2 × 3 × 5 × 5 × 5) = 14.4225. Therefore, the value of the cube root of 3000 is 14.4225.

Is 3000 a Perfect Cube?

The number 3000 on prime factorization gives 2 × 2 × 2 × 3 × 5 × 5 × 5. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 3000 is irrational, hence 3000 is not a perfect cube.

What is the Cube of the Cube Root of 3000?

The cube of the cube root of 3000 is the number 3000 itself i.e. (∛3000)3 = (30001/3)3 = 3000.

What is the Cube Root of -3000?

The cube root of -3000 is equal to the negative of the cube root of 3000. Therefore, ∛-3000 = -(∛3000) = -(14.422) = -14.422.

How to Simplify the Cube Root of 3000/27?

We know that the cube root of 3000 is 14.4225 and the cube root of 27 is 3. Therefore, ∛(3000/27) = (∛3000)/(∛27) = 14.422/3 = 4.8073.

Why is the Value of the Cube Root of 3000 Irrational?

The value of the cube root of 3000 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛3000 is irrational.

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