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Cube Root of 57

The value of the cube root of 57 rounded to 4 decimal places is 3.8485. It is the real solution of the equation x³ = 57. The cube root of 57 is expressed as ∛57 in the radical form and as (57)^⅓ or (57)^0.33 in the exponent form. The prime factorization of 57 is 3 × 19, hence, the cube root of 57 in its lowest radical form is expressed as ∛57.

Cube root of 57: 3.848501131
Cube root of 57 in Exponential Form: (57)^⅓
Cube root of 57 in Radical Form: ∛57

1.	What is the Cube Root of 57?
2.	How to Calculate the Cube Root of 57?
3.	Is the Cube Root of 57 Irrational?
4.	FAQs on Cube Root of 57

What is the Cube Root of 57?

The cube root of 57 is the number which when multiplied by itself three times gives the product as 57. Since 57 can be expressed as 3 × 19. Therefore, the cube root of 57 = ∛(3 × 19) = 3.8485.

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How to Calculate the Value of the Cube Root of 57?

Cube Root of 57 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 = 57
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 57]
⇒ x = 3
Therefore,
∛57 = 3 (3³ + 2 × 57)/(2 × 3³ + 57)) = 3.81
⇒ ∛57 ≈ 3.81
Therefore, the cube root of 57 is 3.81 approximately.

Is the Cube Root of 57 Irrational?

Yes, because ∛57 = ∛(3 × 19) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 57 is an irrational number.

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Cube Root of 57 Solved Examples

Example 1: What is the value of ∛57 ÷ ∛(-57)?

Solution:

The cube root of -57 is equal to the negative of the cube root of 57.
⇒ ∛-57 = -∛57

Therefore,
⇒ ∛57/∛(-57) = ∛57/(-∛57) = -1
Example 2: The volume of a spherical ball is 57π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 57π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 57
⇒ R = ∛(3/4 × 57) = ∛(3/4) × ∛57 = 0.90856 × 3.8485 (∵ ∛(3/4) = 0.90856 and ∛57 = 3.8485)
⇒ R = 3.49659 in³
Example 3: Given the volume of a cube is 57 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 57 in³ = a³
⇒ a³ = 57
Cube rooting on both sides,
⇒ a = ∛57 in
Since the cube root of 57 is 3.85, therefore, the length of the side of the cube is 3.85 in.

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FAQs on Cube Root of 57

What is the Value of the Cube Root of 57?

We can express 57 as 3 × 19 i.e. ∛57 = ∛(3 × 19) = 3.8485. Therefore, the value of the cube root of 57 is 3.8485.

What is the Cube of the Cube Root of 57?

The cube of the cube root of 57 is the number 57 itself i.e. (∛57)³ = (57^1/3)³ = 57.

What is the Value of 16 Plus 2 Cube Root 57?

The value of ∛57 is 3.849. So, 16 + 2 × ∛57 = 16 + 2 × 3.849 = 23.698. Hence, the value of 16 plus 2 cube root 57 is 23.698.

How to Simplify the Cube Root of 57/125?

We know that the cube root of 57 is 3.8485 and the cube root of 125 is 5. Therefore, ∛(57/125) = (∛57)/(∛125) = 3.849/5 = 0.7698.

Why is the Value of the Cube Root of 57 Irrational?

The value of the cube root of 57 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛57 is irrational.

Is 57 a Perfect Cube?

The number 57 on prime factorization gives 3 × 19. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 57 is irrational, hence 57 is not a perfect cube.