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Cube Root of 120

The value of the cube root of 120 rounded to 6 decimal places is 4.932424. It is the real solution of the equation x³ = 120. The cube root of 120 is expressed as ∛120 or 2 ∛15 in the radical form and as (120)^⅓ or (120)^0.33 in the exponent form. The prime factorization of 120 is 2 × 2 × 2 × 3 × 5, hence, the cube root of 120 in its lowest radical form is expressed as 2 ∛15.

Cube root of 120: 4.932424149
Cube root of 120 in Exponential Form: (120)^⅓
Cube root of 120 in Radical Form: ∛120 or 2 ∛15

Cube Root of 120

1.	What is the Cube Root of 120?
2.	How to Calculate the Cube Root of 120?
3.	Is the Cube Root of 120 Irrational?
4.	FAQs on Cube Root of 120

What is the Cube Root of 120?

The cube root of 120 is the number which when multiplied by itself three times gives the product as 120. Since 120 can be expressed as 2 × 2 × 2 × 3 × 5. Therefore, the cube root of 120 = ∛(2 × 2 × 2 × 3 × 5) = 4.9324.

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How to Calculate the Value of the Cube Root of 120?

Cube Root of 120 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 = 120
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 120]
⇒ x = 4
Therefore,
∛120 = 4 (4³ + 2 × 120)/(2 × 4³ + 120)) = 4.9
⇒ ∛120 ≈ 4.9
Therefore, the cube root of 120 is 4.9 approximately.

Is the Cube Root of 120 Irrational?

Yes, because ∛120 = ∛(2 × 2 × 2 × 3 × 5) = 2 ∛15 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 120 is an irrational number.

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Cube Root of 120 Solved Examples

Example 1: The volume of a spherical ball is 120π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 120π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 120
⇒ R = ∛(3/4 × 120) = ∛(3/4) × ∛120 = 0.90856 × 4.93242 (∵ ∛(3/4) = 0.90856 and ∛120 = 4.93242)
⇒ R = 4.4814 in³
Example 2: Find the real root of the equation x³ − 120 = 0.

Solution:

x³ − 120 = 0 i.e. x³ = 120
Solving for x gives us,
x = ∛120, x = ∛120 × (-1 + √3i))/2 and x = ∛120 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛120
Therefore, the real root of the equation x³ − 120 = 0 is for x = ∛120 = 4.9324.
Example 3: What is the value of ∛120 + ∛(-120)?

Solution:

The cube root of -120 is equal to the negative of the cube root of 120.
i.e. ∛-120 = -∛120

Therefore, ∛120 + ∛(-120) = ∛120 - ∛120 = 0

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FAQs on Cube Root of 120

What is the Value of the Cube Root of 120?

We can express 120 as 2 × 2 × 2 × 3 × 5 i.e. ∛120 = ∛(2 × 2 × 2 × 3 × 5) = 4.93242. Therefore, the value of the cube root of 120 is 4.93242.

If the Cube Root of 120 is 4.93, Find the Value of ∛0.12.

Let us represent ∛0.12 in p/q form i.e. ∛(120/1000) = 4.93/10 = 0.49. Hence, the value of ∛0.12 = 0.49.

Why is the Value of the Cube Root of 120 Irrational?

The value of the cube root of 120 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛120 is irrational.

What is the Cube Root of -120?

The cube root of -120 is equal to the negative of the cube root of 120. Therefore, ∛-120 = -(∛120) = -(4.932) = -4.932.

What is the Value of 9 Plus 3 Cube Root 120?

The value of ∛120 is 4.932. So, 9 + 3 × ∛120 = 9 + 3 × 4.932 = 23.796. Hence, the value of 9 plus 3 cube root 120 is 23.796.

Is 120 a Perfect Cube?

The number 120 on prime factorization gives 2 × 2 × 2 × 3 × 5. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 120 is irrational, hence 120 is not a perfect cube.

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