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Cube Root of 1029

The value of the cube root of 1029 rounded to 6 decimal places is 10.095747. It is the real solution of the equation x³ = 1029. The cube root of 1029 is expressed as ∛1029 or 7 ∛3 in the radical form and as (1029)^⅓ or (1029)^0.33 in the exponent form. The prime factorization of 1029 is 3 × 7 × 7 × 7, hence, the cube root of 1029 in its lowest radical form is expressed as 7 ∛3.

Cube root of 1029: 10.095746992
Cube root of 1029 in Exponential Form: (1029)^⅓
Cube root of 1029 in Radical Form: ∛1029 or 7 ∛3

Cube Root of 1029

1.	What is the Cube Root of 1029?
2.	How to Calculate the Cube Root of 1029?
3.	Is the Cube Root of 1029 Irrational?
4.	FAQs on Cube Root of 1029

What is the Cube Root of 1029?

The cube root of 1029 is the number which when multiplied by itself three times gives the product as 1029. Since 1029 can be expressed as 3 × 7 × 7 × 7. Therefore, the cube root of 1029 = ∛(3 × 7 × 7 × 7) = 10.0957.

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How to Calculate the Value of the Cube Root of 1029?

Cube Root of 1029 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 = 1029
Let us assume x as 10
[∵ 10³ = 1000 and 1000 is the nearest perfect cube that is less than 1029]
⇒ x = 10
Therefore,
∛1029 = 10 (10³ + 2 × 1029)/(2 × 10³ + 1029)) = 10.1
⇒ ∛1029 ≈ 10.1
Therefore, the cube root of 1029 is 10.1 approximately.

Is the Cube Root of 1029 Irrational?

Yes, because ∛1029 = ∛(3 × 7 × 7 × 7) = 7 ∛3 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 1029 is an irrational number.

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Cube Root of 1029 Solved Examples

Example 1: Given the volume of a cube is 1029 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 1029 in³ = a³
⇒ a³ = 1029
Cube rooting on both sides,
⇒ a = ∛1029 in
Since the cube root of 1029 is 10.1, therefore, the length of the side of the cube is 10.1 in.
Example 2: What is the value of ∛1029 + ∛(-1029)?

Solution:

The cube root of -1029 is equal to the negative of the cube root of 1029.
i.e. ∛-1029 = -∛1029

Therefore, ∛1029 + ∛(-1029) = ∛1029 - ∛1029 = 0
Example 3: Find the real root of the equation x³ − 1029 = 0.

Solution:

x³ − 1029 = 0 i.e. x³ = 1029
Solving for x gives us,
x = ∛1029, x = ∛1029 × (-1 + √3i))/2 and x = ∛1029 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛1029
Therefore, the real root of the equation x³ − 1029 = 0 is for x = ∛1029 = 10.0957.

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FAQs on Cube Root of 1029

What is the Value of the Cube Root of 1029?

We can express 1029 as 3 × 7 × 7 × 7 i.e. ∛1029 = ∛(3 × 7 × 7 × 7) = 10.09575. Therefore, the value of the cube root of 1029 is 10.09575.

What is the Cube of the Cube Root of 1029?

The cube of the cube root of 1029 is the number 1029 itself i.e. (∛1029)³ = (1029^1/3)³ = 1029.

Is 1029 a Perfect Cube?

The number 1029 on prime factorization gives 3 × 7 × 7 × 7. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 1029 is irrational, hence 1029 is not a perfect cube.

How to Simplify the Cube Root of 1029/216?

We know that the cube root of 1029 is 10.09575 and the cube root of 216 is 6. Therefore, ∛(1029/216) = (∛1029)/(∛216) = 10.096/6 = 1.6827.

If the Cube Root of 1029 is 10.1, Find the Value of ∛1.029.

Let us represent ∛1.029 in p/q form i.e. ∛(1029/1000) = 10.1/10 = 1.01. Hence, the value of ∛1.029 = 1.01.

Why is the Value of the Cube Root of 1029 Irrational?

The value of the cube root of 1029 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛1029 is irrational.

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