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Cube Root of 294

The value of the cube root of 294 rounded to 5 decimal places is 6.6494. It is the real solution of the equation x³ = 294. The cube root of 294 is expressed as ∛294 in the radical form and as (294)^⅓ or (294)^0.33 in the exponent form. The prime factorization of 294 is 2 × 3 × 7 × 7, hence, the cube root of 294 in its lowest radical form is expressed as ∛294.

Cube root of 294: 6.649399761
Cube root of 294 in Exponential Form: (294)^⅓
Cube root of 294 in Radical Form: ∛294

Cube Root of 294

1.	What is the Cube Root of 294?
2.	How to Calculate the Cube Root of 294?
3.	Is the Cube Root of 294 Irrational?
4.	FAQs on Cube Root of 294

What is the Cube Root of 294?

The cube root of 294 is the number which when multiplied by itself three times gives the product as 294. Since 294 can be expressed as 2 × 3 × 7 × 7. Therefore, the cube root of 294 = ∛(2 × 3 × 7 × 7) = 6.6494.

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How to Calculate the Value of the Cube Root of 294?

Cube Root of 294 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 = 294
Let us assume x as 6
[∵ 6³ = 216 and 216 is the nearest perfect cube that is less than 294]
⇒ x = 6
Therefore,
∛294 = 6 (6³ + 2 × 294)/(2 × 6³ + 294)) = 6.64
⇒ ∛294 ≈ 6.64
Therefore, the cube root of 294 is 6.64 approximately.

Is the Cube Root of 294 Irrational?

Yes, because ∛294 = ∛(2 × 3 × 7 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 294 is an irrational number.

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Cube Root of 294 Solved Examples

Example 1: What is the value of ∛294 + ∛(-294)?

Solution:

The cube root of -294 is equal to the negative of the cube root of 294.
i.e. ∛-294 = -∛294

Therefore, ∛294 + ∛(-294) = ∛294 - ∛294 = 0
Example 2: The volume of a spherical ball is 294π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 294π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 294
⇒ R = ∛(3/4 × 294) = ∛(3/4) × ∛294 = 0.90856 × 6.6494 (∵ ∛(3/4) = 0.90856 and ∛294 = 6.6494)
⇒ R = 6.04138 in³
Example 3: Find the real root of the equation x³ − 294 = 0.

Solution:

x³ − 294 = 0 i.e. x³ = 294
Solving for x gives us,
x = ∛294, x = ∛294 × (-1 + √3i))/2 and x = ∛294 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛294
Therefore, the real root of the equation x³ − 294 = 0 is for x = ∛294 = 6.6494.

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FAQs on Cube Root of 294

What is the Value of the Cube Root of 294?

We can express 294 as 2 × 3 × 7 × 7 i.e. ∛294 = ∛(2 × 3 × 7 × 7) = 6.6494. Therefore, the value of the cube root of 294 is 6.6494.

If the Cube Root of 294 is 6.65, Find the Value of ∛0.294.

Let us represent ∛0.294 in p/q form i.e. ∛(294/1000) = 6.65/10 = 0.66. Hence, the value of ∛0.294 = 0.66.

What is the Cube of the Cube Root of 294?

The cube of the cube root of 294 is the number 294 itself i.e. (∛294)³ = (294^1/3)³ = 294.

What is the Cube Root of -294?

The cube root of -294 is equal to the negative of the cube root of 294. Therefore, ∛-294 = -(∛294) = -(6.649) = -6.649.

Is 294 a Perfect Cube?

The number 294 on prime factorization gives 2 × 3 × 7 × 7. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 294 is irrational, hence 294 is not a perfect cube.

How to Simplify the Cube Root of 294/8?

We know that the cube root of 294 is 6.6494 and the cube root of 8 is 2. Therefore, ∛(294/8) = (∛294)/(∛8) = 6.649/2 = 3.3245.

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