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Cube Root of 200

The value of the cube root of 200 rounded to 7 decimal places is 5.8480355. It is the real solution of the equation x³ = 200. The cube root of 200 is expressed as ∛200 or 2 ∛25 in the radical form and as (200)^⅓ or (200)^0.33 in the exponent form. The prime factorization of 200 is 2 × 2 × 2 × 5 × 5, hence, the cube root of 200 in its lowest radical form is expressed as 2 ∛25.

Cube root of 200: 5.848035476
Cube root of 200 in Exponential Form: (200)^⅓
Cube root of 200 in Radical Form: ∛200 or 2 ∛25

Cube Root of 200

1.	What is the Cube Root of 200?
2.	How to Calculate the Cube Root of 200?
3.	Is the Cube Root of 200 Irrational?
4.	FAQs on Cube Root of 200

What is the Cube Root of 200?

The cube root of 200 is the number which when multiplied by itself three times gives the product as 200. Since 200 can be expressed as 2 × 2 × 2 × 5 × 5. Therefore, the cube root of 200 = ∛(2 × 2 × 2 × 5 × 5) = 5.848.

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How to Calculate the Value of the Cube Root of 200?

Cube Root of 200 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 = 200
Let us assume x as 5
[∵ 5³ = 125 and 125 is the nearest perfect cube that is less than 200]
⇒ x = 5
Therefore,
∛200 = 5 (5³ + 2 × 200)/(2 × 5³ + 200)) = 5.83
⇒ ∛200 ≈ 5.83
Therefore, the cube root of 200 is 5.83 approximately.

Is the Cube Root of 200 Irrational?

Yes, because ∛200 = ∛(2 × 2 × 2 × 5 × 5) = 2 ∛25 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 200 is an irrational number.

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Cube Root of 200 Solved Examples

Example 1: What is the value of ∛200 + ∛(-200)?

Solution:

The cube root of -200 is equal to the negative of the cube root of 200.
i.e. ∛-200 = -∛200

Therefore, ∛200 + ∛(-200) = ∛200 - ∛200 = 0
Example 2: The volume of a spherical ball is 200π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 200π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 200
⇒ R = ∛(3/4 × 200) = ∛(3/4) × ∛200 = 0.90856 × 5.84804 (∵ ∛(3/4) = 0.90856 and ∛200 = 5.84804)
⇒ R = 5.3133 in³
Example 3: Find the real root of the equation x³ − 200 = 0.

Solution:

x³ − 200 = 0 i.e. x³ = 200
Solving for x gives us,
x = ∛200, x = ∛200 × (-1 + √3i))/2 and x = ∛200 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛200
Therefore, the real root of the equation x³ − 200 = 0 is for x = ∛200 = 5.848.

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FAQs on Cube Root of 200

What is the Value of the Cube Root of 200?

We can express 200 as 2 × 2 × 2 × 5 × 5 i.e. ∛200 = ∛(2 × 2 × 2 × 5 × 5) = 5.84804. Therefore, the value of the cube root of 200 is 5.84804.

How to Simplify the Cube Root of 200/729?

We know that the cube root of 200 is 5.84804 and the cube root of 729 is 9. Therefore, ∛(200/729) = (∛200)/(∛729) = 5.848/9 = 0.6498.

What is the Value of 1 Plus 6 Cube Root 200?

The value of ∛200 is 5.848. So, 1 + 6 × ∛200 = 1 + 6 × 5.848 = 36.088. Hence, the value of 1 plus 6 cube root 200 is 36.088.

Why is the Value of the Cube Root of 200 Irrational?

The value of the cube root of 200 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛200 is irrational.

What is the Cube Root of -200?

The cube root of -200 is equal to the negative of the cube root of 200. Therefore, ∛-200 = -(∛200) = -(5.848) = -5.848.

Is 200 a Perfect Cube?

The number 200 on prime factorization gives 2 × 2 × 2 × 5 × 5. Here, the prime factor 5 is not in the power of 3. Therefore the cube root of 200 is irrational, hence 200 is not a perfect cube.

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