Cube Root of 238 - How to Find the Cube Root of 238? [Solved] (2024)

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

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.

☛ Check: Cube Root Calculator

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.

☛ Also Check:

Cube Root of 3
Cube Root of 432
Cube Root of 80
Cube Root of 196
Cube Root of 24
Cube Root of 42
Cube Root of 2

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

Show Solution >

go to slidego to slidego to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

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.

FAQs

Cube Root of 238 - How to Find the Cube Root of 238? [Solved]? ›

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.

View Details ›

How do you find the cube root of a solution? ›

It can be calculated by first finding out the prime factorization of the given number and then later applying the cube root formula. Suppose, x is any number such that, x = y × y × y. The formula to calculate the cube root is given as: Cube root of x = ∛x = ∛(y × y × y) = y.

Explore More ›

How to find cube root calculator? ›

If your calculator doesn't have a cube root button, you can use the exponentiation button (usually marked as "^") and enter the fraction 1/3. 3. Press the "=" button to get the result. For example, to find the cube root of 8, you would enter "8", press the "∛" button (or "^" and then "1/3"), and then press "=".

Keep Reading ›

How to find cube formula? ›

The cube of a number is a number that is obtained when a number is multiplied thrice by itself. For example, cube of 2 is 2 × 2 × 2 = 8.

Learn More Now ›

How do you find the root solution? ›

Important Formulas on Roots of Quadratic Equations:

The roots are calculated using the formula, x = (-b ± √ (b² - 4ac) )/2a.
Discriminant is, D = b² - 4ac. If D > 0, then the equation has two real and distinct roots. If D < 0, the equation has two complex roots. ...
Sum of the roots = -b/a.
Product of the roots = c/a.

Get More Info ›

How do you find the cube root code? ›

Algorithm

Take a cubic number x as input.
Use cbrt( x ) to calculate the cube root of x.
Return result.

Oct 17, 2022

Know More ›

How do you work out cubed? ›

For example 3 x 3 x 3 = 27. An easy way to write 3 cubed is 3³. This means three multiplied by itself three times. The easiest way to do this calculation is to do the first multiplication (3x3) and then to multiply your answer by the same number you started with; 3 x 3 x 3 = 9 x 3 = 27.

View Details ›

Does 27 make a perfect cube? ›

Yes, 27 is a perfect cube number since the cube root value of 27 is a whole number.

How to find the perfect cube? ›

The perfect cube is the result of multiplying the same integer three times. Multiplying the number 4 three times, for example, yields 64. As a result, the number 64 is a perfect cube. Perfect cube = number x number x number.

Find Out More ›

How do you solve a cube without a formula? ›

It can be broken down into solving the edges and corners separately: doing this by orienting and permuting both the edges and corners. Orienting means that the pieces are facing the correct way and permuting means the pieces are in their correct, solved location.

View Details ›

Is there a trick to finding cube roots? ›

Cube root of a number can be found by a very simple method which is the prime factorization method. Cube root is denoted by '∛ ' symbol. Example: ∛8 = ∛(2 × 2 × 2) = 2. Since, 8 is a perfect cube number, it is easy to find the cube root of a number.

Show Me More ›

How to find cube root 3? ›

The value of the cube root of 3 is equal to 1.44224957031. Cube root of 3 in radical form is represented as ³√3 and in exponential form as 3¹^/³. Since 3 is not a perfect cube, therefore it is a little difficult to find its cube root.

How do you find the roots of a cube equation? ›

The values of 'x' that satisfy the equation p(x) = 0 are called roots of cubic polynomial p(x). Since the degree of p(x), the cubic equation p(x) = 0 can have a maximum of 3 roots. The roots of a cubic equation can be found by using synthetic division, factoring, or rational root theorem.

Explore More ›

What is the formula for the cube root function? ›

What is the Formula of Cube Root Function? The formula for basic (parent) cube root function is f(x) = ∛x. It can also be of the form f(x) = a ∛(bx - h) + k after the transformations. Here, a, b, h, and k are real numbers and they represent the transformations.

Read The Full Story ›

How do you find the cube root of a product? ›

Using Prime Factorization

Step 1: Factor the number into its prime factors. For example, for 216, the factorization is 2³×3³.
Step 2: Group the factors into triples. Here, 2³ and 3³are already grouped.
Step 3: Take one factor from each group. The cube root of 2³×3³ is 2×3=6.

May 27, 2024

Explore More ›

How to calculate the cube root of 1331? ›

The cube root of 1331 is the number which when multiplied by itself three times gives the product as 1331. Since 1331 can be expressed as 11 × 11 × 11. Therefore, the cube root of 1331 = ∛(11 × 11 × 11) = 11.