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Cube Root of 238

The value of the cube root of 238 rounded to 5 decimal places is 6.19715. It is the real solution of the equation x³ = 238. The cube root of 238 is expressed as ∛238 in the radical form and as (238)^⅓ or (238)^0.33 in the exponent form. The prime factorization of 238 is 2 × 7 × 17, hence, the cube root of 238 in its lowest radical form is expressed as ∛238.

Cube root of 238: 6.197154435
Cube root of 238 in Exponential Form: (238)^⅓
Cube root of 238 in Radical Form: ∛238

Cube Root of 238

1.	What is the Cube Root of 238?
2.	How to Calculate the Cube Root of 238?
3.	Is the Cube Root of 238 Irrational?
4.	FAQs on Cube Root of 238

What is the Cube Root of 238?

The cube root of 238 is the number which when multiplied by itself three times gives the product as 238. Since 238 can be expressed as 2 × 7 × 17. Therefore, the cube root of 238 = ∛(2 × 7 × 17) = 6.1972.

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How to Calculate the Value of the Cube Root of 238?

Cube Root of 238 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 = 238
Let us assume x as 6
[∵ 6³ = 216 and 216 is the nearest perfect cube that is less than 238]
⇒ x = 6
Therefore,
∛238 = 6 (6³ + 2 × 238)/(2 × 6³ + 238)) = 6.2
⇒ ∛238 ≈ 6.2
Therefore, the cube root of 238 is 6.2 approximately.

Is the Cube Root of 238 Irrational?

Yes, because ∛238 = ∛(2 × 7 × 17) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 238 is an irrational number.

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Cube Root of 238 Solved Examples

Example 1: What is the value of ∛238 + ∛(-238)?

Solution:

The cube root of -238 is equal to the negative of the cube root of 238.
i.e. ∛-238 = -∛238

Therefore, ∛238 + ∛(-238) = ∛238 - ∛238 = 0
Example 2: Find the real root of the equation x³ − 238 = 0.

Solution:

x³ − 238 = 0 i.e. x³ = 238
Solving for x gives us,
x = ∛238, x = ∛238 × (-1 + √3i))/2 and x = ∛238 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛238
Therefore, the real root of the equation x³ − 238 = 0 is for x = ∛238 = 6.1972.
Example 3: The volume of a spherical ball is 238π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 238π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 238
⇒ R = ∛(3/4 × 238) = ∛(3/4) × ∛238 = 0.90856 × 6.19715 (∵ ∛(3/4) = 0.90856 and ∛238 = 6.19715)
⇒ R = 5.63048 in³

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FAQs on Cube Root of 238

What is the Value of the Cube Root of 238?

We can express 238 as 2 × 7 × 17 i.e. ∛238 = ∛(2 × 7 × 17) = 6.19715. Therefore, the value of the cube root of 238 is 6.19715.

What is the Value of 3 Plus 11 Cube Root 238?

The value of ∛238 is 6.197. So, 3 + 11 × ∛238 = 3 + 11 × 6.197 = 71.167. Hence, the value of 3 plus 11 cube root 238 is 71.167.

How to Simplify the Cube Root of 238/27?

We know that the cube root of 238 is 6.19715 and the cube root of 27 is 3. Therefore, ∛(238/27) = (∛238)/(∛27) = 6.197/3 = 2.0657.

Is 238 a Perfect Cube?

The number 238 on prime factorization gives 2 × 7 × 17. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 238 is irrational, hence 238 is not a perfect cube.

What is the Cube of the Cube Root of 238?

The cube of the cube root of 238 is the number 238 itself i.e. (∛238)³ = (238^1/3)³ = 238.

What is the Cube Root of -238?

The cube root of -238 is equal to the negative of the cube root of 238. Therefore, ∛-238 = -(∛238) = -(6.197) = -6.197.

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