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Cube Root of 60

The value of the cube root of 60 rounded to 4 decimal places is 3.9149. It is the real solution of the equation x³ = 60. The cube root of 60 is expressed as ∛60 in the radical form and as (60)^⅓ or (60)^0.33 in the exponent form. The prime factorization of 60 is 2 × 2 × 3 × 5, hence, the cube root of 60 in its lowest radical form is expressed as ∛60.

Cube root of 60: 3.914867641
Cube root of 60 in Exponential Form: (60)^⅓
Cube root of 60 in Radical Form: ∛60

1.	What is the Cube Root of 60?
2.	How to Calculate the Cube Root of 60?
3.	Is the Cube Root of 60 Irrational?
4.	FAQs on Cube Root of 60

What is the Cube Root of 60?

The cube root of 60 is the number which when multiplied by itself three times gives the product as 60. Since 60 can be expressed as 2 × 2 × 3 × 5. Therefore, the cube root of 60 = ∛(2 × 2 × 3 × 5) = 3.9149.

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How to Calculate the Value of the Cube Root of 60?

Cube Root of 60 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 = 60
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 60]
⇒ x = 3
Therefore,
∛60 = 3 (3³ + 2 × 60)/(2 × 3³ + 60)) = 3.87
⇒ ∛60 ≈ 3.87
Therefore, the cube root of 60 is 3.87 approximately.

Is the Cube Root of 60 Irrational?

Yes, because ∛60 = ∛(2 × 2 × 3 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 60 is an irrational number.

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Cube Root of 60 Solved Examples

Example 1: Given the volume of a cube is 60 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 60 in³ = a³
⇒ a³ = 60
Cube rooting on both sides,
⇒ a = ∛60 in
Since the cube root of 60 is 3.91, therefore, the length of the side of the cube is 3.91 in.
Example 2: The volume of a spherical ball is 60π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 60π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 60
⇒ R = ∛(3/4 × 60) = ∛(3/4) × ∛60 = 0.90856 × 3.91487 (∵ ∛(3/4) = 0.90856 and ∛60 = 3.91487)
⇒ R = 3.55689 in³
Example 3: What is the value of ∛60 + ∛(-60)?

Solution:

The cube root of -60 is equal to the negative of the cube root of 60.
i.e. ∛-60 = -∛60

Therefore, ∛60 + ∛(-60) = ∛60 - ∛60 = 0

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FAQs on Cube Root of 60

What is the Value of the Cube Root of 60?

We can express 60 as 2 × 2 × 3 × 5 i.e. ∛60 = ∛(2 × 2 × 3 × 5) = 3.91487. Therefore, the value of the cube root of 60 is 3.91487.

What is the Cube of the Cube Root of 60?

The cube of the cube root of 60 is the number 60 itself i.e. (∛60)³ = (60^1/3)³ = 60.

How to Simplify the Cube Root of 60/125?

We know that the cube root of 60 is 3.91487 and the cube root of 125 is 5. Therefore, ∛(60/125) = (∛60)/(∛125) = 3.915/5 = 0.783.

Is 60 a Perfect Cube?

The number 60 on prime factorization gives 2 × 2 × 3 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 60 is irrational, hence 60 is not a perfect cube.

What is the Value of 20 Plus 3 Cube Root 60?

The value of ∛60 is 3.915. So, 20 + 3 × ∛60 = 20 + 3 × 3.915 = 31.745. Hence, the value of 20 plus 3 cube root 60 is 31.745.

If the Cube Root of 60 is 3.91, Find the Value of ∛0.06.

Let us represent ∛0.06 in p/q form i.e. ∛(60/1000) = 3.91/10 = 0.39. Hence, the value of ∛0.06 = 0.39.