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Cube Root of 2304

The value of the cube root of 2304 rounded to 7 decimal places is 13.207709. It is the real solution of the equation x³ = 2304. The cube root of 2304 is expressed as ∛2304 or 4 ∛36 in the radical form and as (2304)^⅓ or (2304)^0.33 in the exponent form. The prime factorization of 2304 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3, hence, the cube root of 2304 in its lowest radical form is expressed as 4 ∛36.

Cube root of 2304: 13.207708996
Cube root of 2304 in Exponential Form: (2304)^⅓
Cube root of 2304 in Radical Form: ∛2304 or 4 ∛36

1.	What is the Cube Root of 2304?
2.	How to Calculate the Cube Root of 2304?
3.	Is the Cube Root of 2304 Irrational?
4.	FAQs on Cube Root of 2304

What is the Cube Root of 2304?

The cube root of 2304 is the number which when multiplied by itself three times gives the product as 2304. Since 2304 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3. Therefore, the cube root of 2304 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3) = 13.2077.

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How to Calculate the Value of the Cube Root of 2304?

Cube Root of 2304 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 = 2304
Let us assume x as 13
[∵ 13³ = 2197 and 2197 is the nearest perfect cube that is less than 2304]
⇒ x = 13
Therefore,
∛2304 = 13 (13³ + 2 × 2304)/(2 × 13³ + 2304)) = 13.21
⇒ ∛2304 ≈ 13.21
Therefore, the cube root of 2304 is 13.21 approximately.

Is the Cube Root of 2304 Irrational?

Yes, because ∛2304 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3) = 4 ∛36 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 2304 is an irrational number.

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Cube Root of 2304 Solved Examples

Example 1: What is the value of ∛2304 + ∛(-2304)?

Solution:

The cube root of -2304 is equal to the negative of the cube root of 2304.
i.e. ∛-2304 = -∛2304

Therefore, ∛2304 + ∛(-2304) = ∛2304 - ∛2304 = 0
Example 2: Given the volume of a cube is 2304 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 2304 in³ = a³
⇒ a³ = 2304
Cube rooting on both sides,
⇒ a = ∛2304 in
Since the cube root of 2304 is 13.21, therefore, the length of the side of the cube is 13.21 in.
Example 3: The volume of a spherical ball is 2304π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 2304π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 2304
⇒ R = ∛(3/4 × 2304) = ∛(3/4) × ∛2304 = 0.90856 × 13.20771 (∵ ∛(3/4) = 0.90856 and ∛2304 = 13.20771)
⇒ R = 12 in³

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FAQs on Cube Root of 2304

What is the Value of the Cube Root of 2304?

We can express 2304 as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 i.e. ∛2304 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3) = 13.20771. Therefore, the value of the cube root of 2304 is 13.20771.

If the Cube Root of 2304 is 13.21, Find the Value of ∛2.304.

Let us represent ∛2.304 in p/q form i.e. ∛(2304/1000) = 13.21/10 = 1.32. Hence, the value of ∛2.304 = 1.32.

What is the Cube Root of -2304?

The cube root of -2304 is equal to the negative of the cube root of 2304. Therefore, ∛-2304 = -(∛2304) = -(13.208) = -13.208.

Is 2304 a Perfect Cube?

The number 2304 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 2304 is irrational, hence 2304 is not a perfect cube.

What is the Cube of the Cube Root of 2304?

The cube of the cube root of 2304 is the number 2304 itself i.e. (∛2304)³ = (2304^1/3)³ = 2304.

How to Simplify the Cube Root of 2304/512?

We know that the cube root of 2304 is 13.20771 and the cube root of 512 is 8. Therefore, ∛(2304/512) = (∛2304)/(∛512) = 13.208/8 = 1.651.