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Cube Root of 11

The value of the cube root of 11 rounded to 6 decimal places is 2.22398. It is the real solution of the equation x³ = 11. The cube root of 11 is expressed as ∛11 in the radical form and as (11)^⅓ or (11)^0.33 in the exponent form. The prime factorization of 11 is 11, hence, the cube root of 11 in its lowest radical form is expressed as ∛11.

Cube root of 11: 2.223980091
Cube root of 11 in Exponential Form: (11)^⅓
Cube root of 11 in Radical Form: ∛11

Cube Root of 11

1.	What is the Cube Root of 11?
2.	How to Calculate the Cube Root of 11?
3.	Is the Cube Root of 11 Irrational?
4.	FAQs on Cube Root of 11

What is the Cube Root of 11?

The cube root of 11 is the number which when multiplied by itself three times gives the product as 11. The number 11 is prime. Therefore, the cube root of 11 = ∛11 = 2.224.

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How to Calculate the Value of the Cube Root of 11?

Cube Root of 11 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 = 11
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 11]
⇒ x = 2
Therefore,
∛11 = 2 (2³ + 2 × 11)/(2 × 2³ + 11)) = 2.22
⇒ ∛11 ≈ 2.22
Therefore, the cube root of 11 is 2.22 approximately.

Is the Cube Root of 11 Irrational?

Yes, because ∛11 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 11 is an irrational number.

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Cube Root of 11 Solved Examples

Example 1: The volume of a spherical ball is 11π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 11π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 11
⇒ R = ∛(3/4 × 11) = ∛(3/4) × ∛11 = 0.90856 × 2.22398 (∵ ∛(3/4) = 0.90856 and ∛11 = 2.22398)
⇒ R = 2.02062 in³
Example 2: Find the real root of the equation x³ − 11 = 0.

Solution:

x³ − 11 = 0 i.e. x³ = 11
Solving for x gives us,
x = ∛11, x = ∛11 × (-1 + √3i))/2 and x = ∛11 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛11
Therefore, the real root of the equation x³ − 11 = 0 is for x = ∛11 = 2.224.
Example 3: Given the volume of a cube is 11 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 11 in³ = a³
⇒ a³ = 11
Cube rooting on both sides,
⇒ a = ∛11 in
Since the cube root of 11 is 2.22, therefore, the length of the side of the cube is 2.22 in.

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FAQs on Cube Root of 11

What is the Value of the Cube Root of 11?

The value of the cube root of 11 is 2.22398.

What is the Cube of the Cube Root of 11?

The cube of the cube root of 11 is the number 11 itself i.e. (∛11)³ = (11^1/3)³ = 11.

Why is the Value of the Cube Root of 11 Irrational?

The value of the cube root of 11 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛11 is irrational.

How to Simplify the Cube Root of 11/27?

We know that the cube root of 11 is 2.22398 and the cube root of 27 is 3. Therefore, ∛(11/27) = (∛11)/(∛27) = 2.224/3 = 0.7413.

If the Cube Root of 11 is 2.22, Find the Value of ∛0.011.

Let us represent ∛0.011 in p/q form i.e. ∛(11/1000) = 2.22/10 = 0.22. Hence, the value of ∛0.011 = 0.22.

Is 11 a Perfect Cube?

The number 11 is prime. Here, the prime factor 11 is not in the power of 3 and this implies that the cube root of 11 is irrational, hence 11 is not a perfect cube.

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