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Cube Root of 1200

The value of the cube root of 1200 rounded to 6 decimal places is 10.626586. It is the real solution of the equation x3 = 1200. The cube root of 1200 is expressed as ∛1200 or 2 ∛150 in the radical form and as (1200)⅓ or (1200)0.33 in the exponent form. The prime factorization of 1200 is 2 × 2 × 2 × 2 × 3 × 5 × 5, hence, the cube root of 1200 in its lowest radical form is expressed as 2 ∛150.

  • Cube root of 1200: 10.626585692
  • Cube root of 1200 in Exponential Form: (1200)⅓
  • Cube root of 1200 in Radical Form: ∛1200 or 2 ∛150

Cube Root of 1200

1. What is the Cube Root of 1200?
2. How to Calculate the Cube Root of 1200?
3. Is the Cube Root of 1200 Irrational?
4. FAQs on Cube Root of 1200

What is the Cube Root of 1200?

The cube root of 1200 is the number which when multiplied by itself three times gives the product as 1200. Since 1200 can be expressed as 2 × 2 × 2 × 2 × 3 × 5 × 5. Therefore, the cube root of 1200 = ∛(2 × 2 × 2 × 2 × 3 × 5 × 5) = 10.6266.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 1200?

Cube Root of 1200 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 = 1200
Let us assume x as 10
[∵ 103 = 1000 and 1000 is the nearest perfect cube that is less than 1200]
⇒ x = 10
Therefore,
∛1200 = 10 (103 + 2 × 1200)/(2 × 103 + 1200)) = 10.62
⇒ ∛1200 ≈ 10.62
Therefore, the cube root of 1200 is 10.62 approximately.

Is the Cube Root of 1200 Irrational?

Yes, because ∛1200 = ∛(2 × 2 × 2 × 2 × 3 × 5 × 5) = 2 ∛150 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 1200 is an irrational number.

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Cube Root of 1200 Solved Examples

  1. Example 1: Find the real root of the equation x3 − 1200 = 0.

    Solution:

    x3 − 1200 = 0 i.e. x3 = 1200
    Solving for x gives us,
    x = ∛1200, x = ∛1200 × (-1 + √3i))/2 and x = ∛1200 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛1200
    Therefore, the real root of the equation x3 − 1200 = 0 is for x = ∛1200 = 10.6266.

  2. Example 2: The volume of a spherical ball is 1200π in3. What is the radius of this ball?

    Solution:

    Volume of the spherical ball = 1200π in3
    = 4/3 × π × R3
    ⇒ R3 = 3/4 × 1200
    ⇒ R = ∛(3/4 × 1200) = ∛(3/4) × ∛1200 = 0.90856 × 10.62659 (∵ ∛(3/4) = 0.90856 and ∛1200 = 10.62659)
    ⇒ R = 9.65489 in3

  3. Example 3: What is the value of ∛1200 ÷ ∛(-1200)?

    Solution:

    The cube root of -1200 is equal to the negative of the cube root of 1200.
    ⇒ ∛-1200 = -∛1200

    Therefore,
    ⇒ ∛1200/∛(-1200) = ∛1200/(-∛1200) = -1

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FAQs on Cube Root of 1200

What is the Value of the Cube Root of 1200?

We can express 1200 as 2 × 2 × 2 × 2 × 3 × 5 × 5 i.e. ∛1200 = ∛(2 × 2 × 2 × 2 × 3 × 5 × 5) = 10.62659. Therefore, the value of the cube root of 1200 is 10.62659.

Is 1200 a Perfect Cube?

The number 1200 on prime factorization gives 2 × 2 × 2 × 2 × 3 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 1200 is irrational, hence 1200 is not a perfect cube.

If the Cube Root of 1200 is 10.63, Find the Value of ∛1.2.

Let us represent ∛1.2 in p/q form i.e. ∛(1200/1000) = 10.63/10 = 1.06. Hence, the value of ∛1.2 = 1.06.

What is the Value of 11 Plus 13 Cube Root 1200?

The value of ∛1200 is 10.627. So, 11 + 13 × ∛1200 = 11 + 13 × 10.627 = 149.151. Hence, the value of 11 plus 13 cube root 1200 is 149.151.

Why is the Value of the Cube Root of 1200 Irrational?

The value of the cube root of 1200 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛1200 is irrational.

How to Simplify the Cube Root of 1200/343?

We know that the cube root of 1200 is 10.62659 and the cube root of 343 is 7. Therefore, ∛(1200/343) = (∛1200)/(∛343) = 10.627/7 = 1.5181.

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