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Cube Root of 121

The value of the cube root of 121 rounded to 7 decimal places is 4.9460874. It is the real solution of the equation x³ = 121. The cube root of 121 is expressed as ∛121 in the radical form and as (121)^⅓ or (121)^0.33 in the exponent form. The prime factorization of 121 is 11 × 11, hence, the cube root of 121 in its lowest radical form is expressed as ∛121.

Cube root of 121: 4.946087443
Cube root of 121 in Exponential Form: (121)^⅓
Cube root of 121 in Radical Form: ∛121

1.	What is the Cube Root of 121?
2.	How to Calculate the Cube Root of 121?
3.	Is the Cube Root of 121 Irrational?
4.	FAQs on Cube Root of 121

What is the Cube Root of 121?

The cube root of 121 is the number which when multiplied by itself three times gives the product as 121. Since 121 can be expressed as 11 × 11. Therefore, the cube root of 121 = ∛(11 × 11) = 4.9461.

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How to Calculate the Value of the Cube Root of 121?

Cube Root of 121 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 = 121
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 121]
⇒ x = 4
Therefore,
∛121 = 4 (4³ + 2 × 121)/(2 × 4³ + 121)) = 4.92
⇒ ∛121 ≈ 4.92
Therefore, the cube root of 121 is 4.92 approximately.

Is the Cube Root of 121 Irrational?

Yes, because ∛121 = ∛(11 × 11) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 121 is an irrational number.

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Cube Root of 121 Solved Examples

Example 1: Find the real root of the equation x³ − 121 = 0.

Solution:

x³ − 121 = 0 i.e. x³ = 121
Solving for x gives us,
x = ∛121, x = ∛121 × (-1 + √3i))/2 and x = ∛121 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛121
Therefore, the real root of the equation x³ − 121 = 0 is for x = ∛121 = 4.9461.
Example 2: The volume of a spherical ball is 121π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 121π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 121
⇒ R = ∛(3/4 × 121) = ∛(3/4) × ∛121 = 0.90856 × 4.94609 (∵ ∛(3/4) = 0.90856 and ∛121 = 4.94609)
⇒ R = 4.49382 in³
Example 3: Given the volume of a cube is 121 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 121 in³ = a³
⇒ a³ = 121
Cube rooting on both sides,
⇒ a = ∛121 in
Since the cube root of 121 is 4.95, therefore, the length of the side of the cube is 4.95 in.

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FAQs on Cube Root of 121

What is the Value of the Cube Root of 121?

We can express 121 as 11 × 11 i.e. ∛121 = ∛(11 × 11) = 4.94609. Therefore, the value of the cube root of 121 is 4.94609.

What is the Cube of the Cube Root of 121?

The cube of the cube root of 121 is the number 121 itself i.e. (∛121)³ = (121^1/3)³ = 121.

How to Simplify the Cube Root of 121/729?

We know that the cube root of 121 is 4.94609 and the cube root of 729 is 9. Therefore, ∛(121/729) = (∛121)/(∛729) = 4.946/9 = 0.5496.

If the Cube Root of 121 is 4.95, Find the Value of ∛0.121.

Let us represent ∛0.121 in p/q form i.e. ∛(121/1000) = 4.95/10 = 0.49. Hence, the value of ∛0.121 = 0.49.

Is 121 a Perfect Cube?

The number 121 on prime factorization gives 11 × 11. Here, the prime factor 11 is not in the power of 3. Therefore the cube root of 121 is irrational, hence 121 is not a perfect cube.

What is the Cube Root of -121?

The cube root of -121 is equal to the negative of the cube root of 121. Therefore, ∛-121 = -(∛121) = -(4.946) = -4.946.