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Cube Root of 576

The value of the cube root of 576 rounded to 5 decimal places is 8.32034. It is the real solution of the equation x³ = 576. The cube root of 576 is expressed as ∛576 or 4 ∛9 in the radical form and as (576)^⅓ or (576)^0.33 in the exponent form. The prime factorization of 576 is 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3, hence, the cube root of 576 in its lowest radical form is expressed as 4 ∛9.

Cube root of 576: 8.320335292
Cube root of 576 in Exponential Form: (576)^⅓
Cube root of 576 in Radical Form: ∛576 or 4 ∛9

Cube Root of 576

1.	What is the Cube Root of 576?
2.	How to Calculate the Cube Root of 576?
3.	Is the Cube Root of 576 Irrational?
4.	FAQs on Cube Root of 576

What is the Cube Root of 576?

The cube root of 576 is the number which when multiplied by itself three times gives the product as 576. Since 576 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3. Therefore, the cube root of 576 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3) = 8.3203.

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How to Calculate the Value of the Cube Root of 576?

Cube Root of 576 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 = 576
Let us assume x as 8
[∵ 8³ = 512 and 512 is the nearest perfect cube that is less than 576]
⇒ x = 8
Therefore,
∛576 = 8 (8³ + 2 × 576)/(2 × 8³ + 576)) = 8.32
⇒ ∛576 ≈ 8.32
Therefore, the cube root of 576 is 8.32 approximately.

Is the Cube Root of 576 Irrational?

Yes, because ∛576 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3) = 4 ∛9 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 576 is an irrational number.

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Cube Root of 576 Solved Examples

Example 1: Find the real root of the equation x³ − 576 = 0.

Solution:

x³ − 576 = 0 i.e. x³ = 576
Solving for x gives us,
x = ∛576, x = ∛576 × (-1 + √3i))/2 and x = ∛576 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛576
Therefore, the real root of the equation x³ − 576 = 0 is for x = ∛576 = 8.3203.
Example 2: Given the volume of a cube is 576 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 576 in³ = a³
⇒ a³ = 576
Cube rooting on both sides,
⇒ a = ∛576 in
Since the cube root of 576 is 8.32, therefore, the length of the side of the cube is 8.32 in.
Example 3: What is the value of ∛576 ÷ ∛(-576)?

Solution:

The cube root of -576 is equal to the negative of the cube root of 576.
⇒ ∛-576 = -∛576

Therefore,
⇒ ∛576/∛(-576) = ∛576/(-∛576) = -1

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FAQs on Cube Root of 576

What is the Value of the Cube Root of 576?

We can express 576 as 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 i.e. ∛576 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3) = 8.32034. Therefore, the value of the cube root of 576 is 8.32034.

What is the Value of 16 Plus 6 Cube Root 576?

The value of ∛576 is 8.32. So, 16 + 6 × ∛576 = 16 + 6 × 8.32 = 65.92. Hence, the value of 16 plus 6 cube root 576 is 65.92.

If the Cube Root of 576 is 8.32, Find the Value of ∛0.576.

Let us represent ∛0.576 in p/q form i.e. ∛(576/1000) = 8.32/10 = 0.83. Hence, the value of ∛0.576 = 0.83.

How to Simplify the Cube Root of 576/125?

We know that the cube root of 576 is 8.32034 and the cube root of 125 is 5. Therefore, ∛(576/125) = (∛576)/(∛125) = 8.32/5 = 1.664.

Why is the Value of the Cube Root of 576 Irrational?

The value of the cube root of 576 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛576 is irrational.

What is the Cube Root of -576?

The cube root of -576 is equal to the negative of the cube root of 576. Therefore, ∛-576 = -(∛576) = -(8.32) = -8.32.

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