Cube Root of 29

The value of the cube root of 29 rounded to 6 decimal places is 3.072317. It is the real solution of the equation x³ = 29. The cube root of 29 is expressed as ∛29 in the radical form and as (29)^⅓ or (29)^0.33 in the exponent form. The prime factorization of 29 is 29, hence, the cube root of 29 in its lowest radical form is expressed as ∛29.

Cube root of 29: 3.072316826
Cube root of 29 in Exponential Form: (29)^⅓
Cube root of 29 in Radical Form: ∛29

Cube Root of 29

1.	What is the Cube Root of 29?
2.	How to Calculate the Cube Root of 29?
3.	Is the Cube Root of 29 Irrational?
4.	FAQs on Cube Root of 29

What is the Cube Root of 29?

The cube root of 29 is the number which when multiplied by itself three times gives the product as 29. The number 29 is prime. Therefore, the cube root of 29 = ∛29 = 3.0723.

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How to Calculate the Value of the Cube Root of 29?

Cube Root of 29 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 = 29
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 29]
⇒ x = 3
Therefore,
∛29 = 3 (3³ + 2 × 29)/(2 × 3³ + 29)) = 3.07
⇒ ∛29 ≈ 3.07
Therefore, the cube root of 29 is 3.07 approximately.

Is the Cube Root of 29 Irrational?

Yes, because ∛29 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 29 is an irrational number.

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Cube Root of 29 Solved Examples

Example 1: Find the real root of the equation x³ − 29 = 0.

Solution:

x³ − 29 = 0 i.e. x³ = 29
Solving for x gives us,
x = ∛29, x = ∛29 × (-1 + √3i))/2 and x = ∛29 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛29
Therefore, the real root of the equation x³ − 29 = 0 is for x = ∛29 = 3.0723.
Example 2: The volume of a spherical ball is 29π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 29π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 29
⇒ R = ∛(3/4 × 29) = ∛(3/4) × ∛29 = 0.90856 × 3.07232 (∵ ∛(3/4) = 0.90856 and ∛29 = 3.07232)
⇒ R = 2.79139 in³
Example 3: What is the value of ∛29 ÷ ∛(-29)?

Solution:

The cube root of -29 is equal to the negative of the cube root of 29.
⇒ ∛-29 = -∛29

Therefore,
⇒ ∛29/∛(-29) = ∛29/(-∛29) = -1

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FAQs on Cube Root of 29

What is the Value of the Cube Root of 29?

The value of the cube root of 29 is 3.07232.

Why is the Value of the Cube Root of 29 Irrational?

The value of the cube root of 29 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛29 is irrational.

Is 29 a Perfect Cube?

The number 29 is prime. Here, the prime factor 29 is not in the power of 3 and this implies that the cube root of 29 is irrational, hence 29 is not a perfect cube.

What is the Cube Root of -29?

The cube root of -29 is equal to the negative of the cube root of 29. Therefore, ∛-29 = -(∛29) = -(3.072) = -3.072.

If the Cube Root of 29 is 3.07, Find the Value of ∛0.029.

Let us represent ∛0.029 in p/q form i.e. ∛(29/1000) = 3.07/10 = 0.31. Hence, the value of ∛0.029 = 0.31.

What is the Cube of the Cube Root of 29?

The cube of the cube root of 29 is the number 29 itself i.e. (∛29)³ = (29^1/3)³ = 29.

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