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Cube Root of 56

The value of the cube root of 56 rounded to 5 decimal places is 3.82586. It is the real solution of the equation x³ = 56. The cube root of 56 is expressed as ∛56 or 2 ∛7 in the radical form and as (56)^⅓ or (56)^0.33 in the exponent form. The prime factorization of 56 is 2 × 2 × 2 × 7, hence, the cube root of 56 in its lowest radical form is expressed as 2 ∛7.

Cube root of 56: 3.825862366
Cube root of 56 in Exponential Form: (56)^⅓
Cube root of 56 in Radical Form: ∛56 or 2 ∛7

1.	What is the Cube Root of 56?
2.	How to Calculate the Cube Root of 56?
3.	Is the Cube Root of 56 Irrational?
4.	FAQs on Cube Root of 56

What is the Cube Root of 56?

The cube root of 56 is the number which when multiplied by itself three times gives the product as 56. Since 56 can be expressed as 2 × 2 × 2 × 7. Therefore, the cube root of 56 = ∛(2 × 2 × 2 × 7) = 3.8259.

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How to Calculate the Value of the Cube Root of 56?

Cube Root of 56 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 = 56
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 56]
⇒ x = 3
Therefore,
∛56 = 3 (3³ + 2 × 56)/(2 × 3³ + 56)) = 3.79
⇒ ∛56 ≈ 3.79
Therefore, the cube root of 56 is 3.79 approximately.

Is the Cube Root of 56 Irrational?

Yes, because ∛56 = ∛(2 × 2 × 2 × 7) = 2 ∛7 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 56 is an irrational number.

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Cube Root of 56 Solved Examples

Example 1: What is the value of ∛56 + ∛(-56)?

Solution:

The cube root of -56 is equal to the negative of the cube root of 56.
i.e. ∛-56 = -∛56

Therefore, ∛56 + ∛(-56) = ∛56 - ∛56 = 0
Example 2: Given the volume of a cube is 56 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 56 in³ = a³
⇒ a³ = 56
Cube rooting on both sides,
⇒ a = ∛56 in
Since the cube root of 56 is 3.83, therefore, the length of the side of the cube is 3.83 in.
Example 3: The volume of a spherical ball is 56π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 56π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 56
⇒ R = ∛(3/4 × 56) = ∛(3/4) × ∛56 = 0.90856 × 3.82586 (∵ ∛(3/4) = 0.90856 and ∛56 = 3.82586)
⇒ R = 3.47602 in³

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FAQs on Cube Root of 56

What is the Value of the Cube Root of 56?

We can express 56 as 2 × 2 × 2 × 7 i.e. ∛56 = ∛(2 × 2 × 2 × 7) = 3.82586. Therefore, the value of the cube root of 56 is 3.82586.

If the Cube Root of 56 is 3.83, Find the Value of ∛0.056.

Let us represent ∛0.056 in p/q form i.e. ∛(56/1000) = 3.83/10 = 0.38. Hence, the value of ∛0.056 = 0.38.

What is the Cube Root of -56?

The cube root of -56 is equal to the negative of the cube root of 56. Therefore, ∛-56 = -(∛56) = -(3.826) = -3.826.

What is the Cube of the Cube Root of 56?

The cube of the cube root of 56 is the number 56 itself i.e. (∛56)³ = (56^1/3)³ = 56.

What is the Value of 20 Plus 4 Cube Root 56?

The value of ∛56 is 3.826. So, 20 + 4 × ∛56 = 20 + 4 × 3.826 = 35.304. Hence, the value of 20 plus 4 cube root 56 is 35.304.

Is 56 a Perfect Cube?

The number 56 on prime factorization gives 2 × 2 × 2 × 7. Here, the prime factor 7 is not in the power of 3. Therefore the cube root of 56 is irrational, hence 56 is not a perfect cube.