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Cube Root of 288

The value of the cube root of 288 rounded to 7 decimal places is 6.6038545. It is the real solution of the equation x³ = 288. The cube root of 288 is expressed as ∛288 or 2 ∛36 in the radical form and as (288)^⅓ or (288)^0.33 in the exponent form. The prime factorization of 288 is 2 × 2 × 2 × 2 × 2 × 3 × 3, hence, the cube root of 288 in its lowest radical form is expressed as 2 ∛36.

Cube root of 288: 6.603854498
Cube root of 288 in Exponential Form: (288)^⅓
Cube root of 288 in Radical Form: ∛288 or 2 ∛36

1.	What is the Cube Root of 288?
2.	How to Calculate the Cube Root of 288?
3.	Is the Cube Root of 288 Irrational?
4.	FAQs on Cube Root of 288

What is the Cube Root of 288?

The cube root of 288 is the number which when multiplied by itself three times gives the product as 288. Since 288 can be expressed as 2 × 2 × 2 × 2 × 2 × 3 × 3. Therefore, the cube root of 288 = ∛(2 × 2 × 2 × 2 × 2 × 3 × 3) = 6.6039.

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How to Calculate the Value of the Cube Root of 288?

Cube Root of 288 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 = 288
Let us assume x as 6
[∵ 6³ = 216 and 216 is the nearest perfect cube that is less than 288]
⇒ x = 6
Therefore,
∛288 = 6 (6³ + 2 × 288)/(2 × 6³ + 288)) = 6.6
⇒ ∛288 ≈ 6.6
Therefore, the cube root of 288 is 6.6 approximately.

Is the Cube Root of 288 Irrational?

Yes, because ∛288 = ∛(2 × 2 × 2 × 2 × 2 × 3 × 3) = 2 ∛36 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 288 is an irrational number.

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Cube Root of 288 Solved Examples

Example 1: The volume of a spherical ball is 288π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 288π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 288
⇒ R = ∛(3/4 × 288) = ∛(3/4) × ∛288 = 0.90856 × 6.60385 (∵ ∛(3/4) = 0.90856 and ∛288 = 6.60385)
⇒ R = 6 in³
Example 2: What is the value of ∛288 + ∛(-288)?

Solution:

The cube root of -288 is equal to the negative of the cube root of 288.
i.e. ∛-288 = -∛288

Therefore, ∛288 + ∛(-288) = ∛288 - ∛288 = 0
Example 3: Given the volume of a cube is 288 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 288 in³ = a³
⇒ a³ = 288
Cube rooting on both sides,
⇒ a = ∛288 in
Since the cube root of 288 is 6.6, therefore, the length of the side of the cube is 6.6 in.

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FAQs on Cube Root of 288

What is the Value of the Cube Root of 288?

We can express 288 as 2 × 2 × 2 × 2 × 2 × 3 × 3 i.e. ∛288 = ∛(2 × 2 × 2 × 2 × 2 × 3 × 3) = 6.60385. Therefore, the value of the cube root of 288 is 6.60385.

How to Simplify the Cube Root of 288/27?

We know that the cube root of 288 is 6.60385 and the cube root of 27 is 3. Therefore, ∛(288/27) = (∛288)/(∛27) = 6.604/3 = 2.2013.

What is the Cube of the Cube Root of 288?

The cube of the cube root of 288 is the number 288 itself i.e. (∛288)³ = (288^1/3)³ = 288.

If the Cube Root of 288 is 6.6, Find the Value of ∛0.288.

Let us represent ∛0.288 in p/q form i.e. ∛(288/1000) = 6.6/10 = 0.66. Hence, the value of ∛0.288 = 0.66.

Is 288 a Perfect Cube?

The number 288 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 288 is irrational, hence 288 is not a perfect cube.

What is the Cube Root of -288?

The cube root of -288 is equal to the negative of the cube root of 288. Therefore, ∛-288 = -(∛288) = -(6.604) = -6.604.