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Cube Root of 1296

The value of the cube root of 1296 rounded to 5 decimal places is 10.90272. It is the real solution of the equation x³ = 1296. The cube root of 1296 is expressed as ∛1296 or 6 ∛6 in the radical form and as (1296)^⅓ or (1296)^0.33 in the exponent form. The prime factorization of 1296 is 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3, hence, the cube root of 1296 in its lowest radical form is expressed as 6 ∛6.

Cube root of 1296: 10.902723557
Cube root of 1296 in Exponential Form: (1296)^⅓
Cube root of 1296 in Radical Form: ∛1296 or 6 ∛6

Cube Root of 1296

1.	What is the Cube Root of 1296?
2.	How to Calculate the Cube Root of 1296?
3.	Is the Cube Root of 1296 Irrational?
4.	FAQs on Cube Root of 1296

What is the Cube Root of 1296?

The cube root of 1296 is the number which when multiplied by itself three times gives the product as 1296. Since 1296 can be expressed as 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3. Therefore, the cube root of 1296 = ∛(2 × 2 × 2 × 2 × 3 × 3 × 3 × 3) = 10.9027.

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How to Calculate the Value of the Cube Root of 1296?

Cube Root of 1296 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 = 1296
Let us assume x as 10
[∵ 10³ = 1000 and 1000 is the nearest perfect cube that is less than 1296]
⇒ x = 10
Therefore,
∛1296 = 10 (10³ + 2 × 1296)/(2 × 10³ + 1296)) = 10.9
⇒ ∛1296 ≈ 10.9
Therefore, the cube root of 1296 is 10.9 approximately.

Is the Cube Root of 1296 Irrational?

Yes, because ∛1296 = ∛(2 × 2 × 2 × 2 × 3 × 3 × 3 × 3) = 6 ∛6 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 1296 is an irrational number.

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Cube Root of 1296 Solved Examples

Example 1: Find the real root of the equation x³ − 1296 = 0.

Solution:

x³ − 1296 = 0 i.e. x³ = 1296
Solving for x gives us,
x = ∛1296, x = ∛1296 × (-1 + √3i))/2 and x = ∛1296 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛1296
Therefore, the real root of the equation x³ − 1296 = 0 is for x = ∛1296 = 10.9027.
Example 2: Given the volume of a cube is 1296 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 1296 in³ = a³
⇒ a³ = 1296
Cube rooting on both sides,
⇒ a = ∛1296 in
Since the cube root of 1296 is 10.9, therefore, the length of the side of the cube is 10.9 in.
Example 3: What is the value of ∛1296 + ∛(-1296)?

Solution:

The cube root of -1296 is equal to the negative of the cube root of 1296.
i.e. ∛-1296 = -∛1296

Therefore, ∛1296 + ∛(-1296) = ∛1296 - ∛1296 = 0

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FAQs on Cube Root of 1296

What is the Value of the Cube Root of 1296?

We can express 1296 as 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 i.e. ∛1296 = ∛(2 × 2 × 2 × 2 × 3 × 3 × 3 × 3) = 10.90272. Therefore, the value of the cube root of 1296 is 10.90272.

What is the Cube of the Cube Root of 1296?

The cube of the cube root of 1296 is the number 1296 itself i.e. (∛1296)³ = (1296^1/3)³ = 1296.

If the Cube Root of 1296 is 10.9, Find the Value of ∛1.296.

Let us represent ∛1.296 in p/q form i.e. ∛(1296/1000) = 10.9/10 = 1.09. Hence, the value of ∛1.296 = 1.09.

What is the Value of 16 Plus 12 Cube Root 1296?

The value of ∛1296 is 10.903. So, 16 + 12 × ∛1296 = 16 + 12 × 10.903 = 146.836. Hence, the value of 16 plus 12 cube root 1296 is 146.836.

What is the Cube Root of -1296?

The cube root of -1296 is equal to the negative of the cube root of 1296. Therefore, ∛-1296 = -(∛1296) = -(10.903) = -10.903.

How to Simplify the Cube Root of 1296/27?

We know that the cube root of 1296 is 10.90272 and the cube root of 27 is 3. Therefore, ∛(1296/27) = (∛1296)/(∛27) = 10.903/3 = 3.6343.

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