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Cube Root of 41

The value of the cube root of 41 rounded to 5 decimal places is 3.44822. It is the real solution of the equation x³ = 41. The cube root of 41 is expressed as ∛41 in the radical form and as (41)^⅓ or (41)^0.33 in the exponent form. The prime factorization of 41 is 41, hence, the cube root of 41 in its lowest radical form is expressed as ∛41.

Cube root of 41: 3.44821724
Cube root of 41 in Exponential Form: (41)^⅓
Cube root of 41 in Radical Form: ∛41

Cube Root of 41

1.	What is the Cube Root of 41?
2.	How to Calculate the Cube Root of 41?
3.	Is the Cube Root of 41 Irrational?
4.	FAQs on Cube Root of 41

What is the Cube Root of 41?

The cube root of 41 is the number which when multiplied by itself three times gives the product as 41. The number 41 is prime. Therefore, the cube root of 41 = ∛41 = 3.4482.

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How to Calculate the Value of the Cube Root of 41?

Cube Root of 41 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 = 41
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 41]
⇒ x = 3
Therefore,
∛41 = 3 (3³ + 2 × 41)/(2 × 3³ + 41)) = 3.44
⇒ ∛41 ≈ 3.44
Therefore, the cube root of 41 is 3.44 approximately.

Is the Cube Root of 41 Irrational?

Yes, because ∛41 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 41 is an irrational number.

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Cube Root of 41 Solved Examples

Example 1: Given the volume of a cube is 41 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 41 in³ = a³
⇒ a³ = 41
Cube rooting on both sides,
⇒ a = ∛41 in
Since the cube root of 41 is 3.45, therefore, the length of the side of the cube is 3.45 in.
Example 2: The volume of a spherical ball is 41π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 41π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 41
⇒ R = ∛(3/4 × 41) = ∛(3/4) × ∛41 = 0.90856 × 3.44822 (∵ ∛(3/4) = 0.90856 and ∛41 = 3.44822)
⇒ R = 3.13291 in³
Example 3: Find the real root of the equation x³ − 41 = 0.

Solution:

x³ − 41 = 0 i.e. x³ = 41
Solving for x gives us,
x = ∛41, x = ∛41 × (-1 + √3i))/2 and x = ∛41 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛41
Therefore, the real root of the equation x³ − 41 = 0 is for x = ∛41 = 3.4482.

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FAQs on Cube Root of 41

What is the Value of the Cube Root of 41?

The value of the cube root of 41 is 3.44822.

How to Simplify the Cube Root of 41/8?

We know that the cube root of 41 is 3.44822 and the cube root of 8 is 2. Therefore, ∛(41/8) = (∛41)/(∛8) = 3.448/2 = 1.724.

Why is the Value of the Cube Root of 41 Irrational?

The value of the cube root of 41 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛41 is irrational.

What is the Cube Root of -41?

The cube root of -41 is equal to the negative of the cube root of 41. Therefore, ∛-41 = -(∛41) = -(3.448) = -3.448.

If the Cube Root of 41 is 3.45, Find the Value of ∛0.041.

Let us represent ∛0.041 in p/q form i.e. ∛(41/1000) = 3.45/10 = 0.34. Hence, the value of ∛0.041 = 0.34.

Is 41 a Perfect Cube?

The number 41 is prime. Here, the prime factor 41 is not in the power of 3 and this implies that the cube root of 41 is irrational, hence 41 is not a perfect cube.

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