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Cube Root of 1080

The value of the cube root of 1080 rounded to 7 decimal places is 10.2598557. It is the real solution of the equation x³ = 1080. The cube root of 1080 is expressed as ∛1080 or 6 ∛5 in the radical form and as (1080)^⅓ or (1080)^0.33 in the exponent form. The prime factorization of 1080 is 2 × 2 × 2 × 3 × 3 × 3 × 5, hence, the cube root of 1080 in its lowest radical form is expressed as 6 ∛5.

Cube root of 1080: 10.25985568
Cube root of 1080 in Exponential Form: (1080)^⅓
Cube root of 1080 in Radical Form: ∛1080 or 6 ∛5

Cube Root of 1080

1.	What is the Cube Root of 1080?
2.	How to Calculate the Cube Root of 1080?
3.	Is the Cube Root of 1080 Irrational?
4.	FAQs on Cube Root of 1080

What is the Cube Root of 1080?

The cube root of 1080 is the number which when multiplied by itself three times gives the product as 1080. Since 1080 can be expressed as 2 × 2 × 2 × 3 × 3 × 3 × 5. Therefore, the cube root of 1080 = ∛(2 × 2 × 2 × 3 × 3 × 3 × 5) = 10.2599.

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How to Calculate the Value of the Cube Root of 1080?

Cube Root of 1080 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 = 1080
Let us assume x as 10
[∵ 10³ = 1000 and 1000 is the nearest perfect cube that is less than 1080]
⇒ x = 10
Therefore,
∛1080 = 10 (10³ + 2 × 1080)/(2 × 10³ + 1080)) = 10.26
⇒ ∛1080 ≈ 10.26
Therefore, the cube root of 1080 is 10.26 approximately.

Is the Cube Root of 1080 Irrational?

Yes, because ∛1080 = ∛(2 × 2 × 2 × 3 × 3 × 3 × 5) = 6 ∛5 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 1080 is an irrational number.

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Cube Root of 1080 Solved Examples

Example 1: Given the volume of a cube is 1080 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 1080 in³ = a³
⇒ a³ = 1080
Cube rooting on both sides,
⇒ a = ∛1080 in
Since the cube root of 1080 is 10.26, therefore, the length of the side of the cube is 10.26 in.
Example 2: Find the real root of the equation x³ − 1080 = 0.

Solution:

x³ − 1080 = 0 i.e. x³ = 1080
Solving for x gives us,
x = ∛1080, x = ∛1080 × (-1 + √3i))/2 and x = ∛1080 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛1080
Therefore, the real root of the equation x³ − 1080 = 0 is for x = ∛1080 = 10.2599.
Example 3: What is the value of ∛1080 ÷ ∛(-1080)?

Solution:

The cube root of -1080 is equal to the negative of the cube root of 1080.
⇒ ∛-1080 = -∛1080

Therefore,
⇒ ∛1080/∛(-1080) = ∛1080/(-∛1080) = -1

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FAQs on Cube Root of 1080

What is the Value of the Cube Root of 1080?

We can express 1080 as 2 × 2 × 2 × 3 × 3 × 3 × 5 i.e. ∛1080 = ∛(2 × 2 × 2 × 3 × 3 × 3 × 5) = 10.25986. Therefore, the value of the cube root of 1080 is 10.25986.

What is the Cube of the Cube Root of 1080?

The cube of the cube root of 1080 is the number 1080 itself i.e. (∛1080)³ = (1080^1/3)³ = 1080.

If the Cube Root of 1080 is 10.26, Find the Value of ∛1.08.

Let us represent ∛1.08 in p/q form i.e. ∛(1080/1000) = 10.26/10 = 1.03. Hence, the value of ∛1.08 = 1.03.

How to Simplify the Cube Root of 1080/125?

We know that the cube root of 1080 is 10.25986 and the cube root of 125 is 5. Therefore, ∛(1080/125) = (∛1080)/(∛125) = 10.26/5 = 2.052.

Is 1080 a Perfect Cube?

The number 1080 on prime factorization gives 2 × 2 × 2 × 3 × 3 × 3 × 5. Here, the prime factor 5 is not in the power of 3. Therefore the cube root of 1080 is irrational, hence 1080 is not a perfect cube.

What is the Cube Root of -1080?

The cube root of -1080 is equal to the negative of the cube root of 1080. Therefore, ∛-1080 = -(∛1080) = -(10.26) = -10.26.

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