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Cube Root of 864

The value of the cube root of 864 rounded to 6 decimal places is 9.524406. It is the real solution of the equation x³ = 864. The cube root of 864 is expressed as ∛864 or 6 ∛4 in the radical form and as (864)^⅓ or (864)^0.33 in the exponent form. The prime factorization of 864 is 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3, hence, the cube root of 864 in its lowest radical form is expressed as 6 ∛4.

Cube root of 864: 9.524406312
Cube root of 864 in Exponential Form: (864)^⅓
Cube root of 864 in Radical Form: ∛864 or 6 ∛4

Cube Root of 864

1.	What is the Cube Root of 864?
2.	How to Calculate the Cube Root of 864?
3.	Is the Cube Root of 864 Irrational?
4.	FAQs on Cube Root of 864

What is the Cube Root of 864?

The cube root of 864 is the number which when multiplied by itself three times gives the product as 864. Since 864 can be expressed as 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3. Therefore, the cube root of 864 = ∛(2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 9.5244.

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How to Calculate the Value of the Cube Root of 864?

Cube Root of 864 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 = 864
Let us assume x as 9
[∵ 9³ = 729 and 729 is the nearest perfect cube that is less than 864]
⇒ x = 9
Therefore,
∛864 = 9 (9³ + 2 × 864)/(2 × 9³ + 864)) = 9.52
⇒ ∛864 ≈ 9.52
Therefore, the cube root of 864 is 9.52 approximately.

Is the Cube Root of 864 Irrational?

Yes, because ∛864 = ∛(2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 6 ∛4 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 864 is an irrational number.

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Cube Root of 864 Solved Examples

Example 1: What is the value of ∛864 + ∛(-864)?

Solution:

The cube root of -864 is equal to the negative of the cube root of 864.
i.e. ∛-864 = -∛864

Therefore, ∛864 + ∛(-864) = ∛864 - ∛864 = 0
Example 2: Find the real root of the equation x³ − 864 = 0.

Solution:

x³ − 864 = 0 i.e. x³ = 864
Solving for x gives us,
x = ∛864, x = ∛864 × (-1 + √3i))/2 and x = ∛864 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛864
Therefore, the real root of the equation x³ − 864 = 0 is for x = ∛864 = 9.5244.
Example 3: The volume of a spherical ball is 864π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 864π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 864
⇒ R = ∛(3/4 × 864) = ∛(3/4) × ∛864 = 0.90856 × 9.52441 (∵ ∛(3/4) = 0.90856 and ∛864 = 9.52441)
⇒ R = 8.6535 in³

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FAQs on Cube Root of 864

What is the Value of the Cube Root of 864?

We can express 864 as 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 i.e. ∛864 = ∛(2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 9.52441. Therefore, the value of the cube root of 864 is 9.52441.

What is the Value of 13 Plus 15 Cube Root 864?

The value of ∛864 is 9.524. So, 13 + 15 × ∛864 = 13 + 15 × 9.524 = 155.85999999999999. Hence, the value of 13 plus 15 cube root 864 is 155.85999999999999.

If the Cube Root of 864 is 9.52, Find the Value of ∛0.864.

Let us represent ∛0.864 in p/q form i.e. ∛(864/1000) = 9.52/10 = 0.95. Hence, the value of ∛0.864 = 0.95.

Is 864 a Perfect Cube?

The number 864 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 864 is irrational, hence 864 is not a perfect cube.

What is the Cube Root of -864?

The cube root of -864 is equal to the negative of the cube root of 864. Therefore, ∛-864 = -(∛864) = -(9.524) = -9.524.

What is the Cube of the Cube Root of 864?

The cube of the cube root of 864 is the number 864 itself i.e. (∛864)³ = (864^1/3)³ = 864.

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