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Cube Root of 14

The value of the cube root of 14 rounded to 4 decimal places is 2.4101. It is the real solution of the equation x³ = 14. The cube root of 14 is expressed as ∛14 in the radical form and as (14)^⅓ or (14)^0.33 in the exponent form. The prime factorization of 14 is 2 × 7, hence, the cube root of 14 in its lowest radical form is expressed as ∛14.

Cube root of 14: 2.410142264
Cube root of 14 in Exponential Form: (14)^⅓
Cube root of 14 in Radical Form: ∛14

Cube Root of 14

1.	What is the Cube Root of 14?
2.	How to Calculate the Cube Root of 14?
3.	Is the Cube Root of 14 Irrational?
4.	FAQs on Cube Root of 14

What is the Cube Root of 14?

The cube root of 14 is the number which when multiplied by itself three times gives the product as 14. Since 14 can be expressed as 2 × 7. Therefore, the cube root of 14 = ∛(2 × 7) = 2.4101.

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How to Calculate the Value of the Cube Root of 14?

Cube Root of 14 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 = 14
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 14]
⇒ x = 2
Therefore,
∛14 = 2 (2³ + 2 × 14)/(2 × 2³ + 14)) = 2.4
⇒ ∛14 ≈ 2.4
Therefore, the cube root of 14 is 2.4 approximately.

Is the Cube Root of 14 Irrational?

Yes, because ∛14 = ∛(2 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 14 is an irrational number.

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Cube Root of 14 Solved Examples

Example 1: Given the volume of a cube is 14 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 14 in³ = a³
⇒ a³ = 14
Cube rooting on both sides,
⇒ a = ∛14 in
Since the cube root of 14 is 2.41, therefore, the length of the side of the cube is 2.41 in.
Example 2: The volume of a spherical ball is 14π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 14π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 14
⇒ R = ∛(3/4 × 14) = ∛(3/4) × ∛14 = 0.90856 × 2.41014 (∵ ∛(3/4) = 0.90856 and ∛14 = 2.41014)
⇒ R = 2.18976 in³
Example 3: Find the real root of the equation x³ − 14 = 0.

Solution:

x³ − 14 = 0 i.e. x³ = 14
Solving for x gives us,
x = ∛14, x = ∛14 × (-1 + √3i))/2 and x = ∛14 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛14
Therefore, the real root of the equation x³ − 14 = 0 is for x = ∛14 = 2.4101.

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FAQs on Cube Root of 14

What is the Value of the Cube Root of 14?

We can express 14 as 2 × 7 i.e. ∛14 = ∛(2 × 7) = 2.41014. Therefore, the value of the cube root of 14 is 2.41014.

Why is the Value of the Cube Root of 14 Irrational?

The value of the cube root of 14 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛14 is irrational.

What is the Cube of the Cube Root of 14?

The cube of the cube root of 14 is the number 14 itself i.e. (∛14)³ = (14^1/3)³ = 14.

Is 14 a Perfect Cube?

The number 14 on prime factorization gives 2 × 7. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 14 is irrational, hence 14 is not a perfect cube.

What is the Value of 3 Plus 17 Cube Root 14?

The value of ∛14 is 2.41. So, 3 + 17 × ∛14 = 3 + 17 × 2.41 = 43.97. Hence, the value of 3 plus 17 cube root 14 is 43.97.

How to Simplify the Cube Root of 14/64?

We know that the cube root of 14 is 2.41014 and the cube root of 64 is 4. Therefore, ∛(14/64) = (∛14)/(∛64) = 2.41/4 = 0.6025.

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