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Cube Root of 55

The value of the cube root of 55 rounded to 6 decimal places is 3.802952. It is the real solution of the equation x³ = 55. The cube root of 55 is expressed as ∛55 in the radical form and as (55)^⅓ or (55)^0.33 in the exponent form. The prime factorization of 55 is 5 × 11, hence, the cube root of 55 in its lowest radical form is expressed as ∛55.

Cube root of 55: 3.802952461
Cube root of 55 in Exponential Form: (55)^⅓
Cube root of 55 in Radical Form: ∛55

1.	What is the Cube Root of 55?
2.	How to Calculate the Cube Root of 55?
3.	Is the Cube Root of 55 Irrational?
4.	FAQs on Cube Root of 55

What is the Cube Root of 55?

The cube root of 55 is the number which when multiplied by itself three times gives the product as 55. Since 55 can be expressed as 5 × 11. Therefore, the cube root of 55 = ∛(5 × 11) = 3.803.

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How to Calculate the Value of the Cube Root of 55?

Cube Root of 55 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 = 55
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 55]
⇒ x = 3
Therefore,
∛55 = 3 (3³ + 2 × 55)/(2 × 3³ + 55)) = 3.77
⇒ ∛55 ≈ 3.77
Therefore, the cube root of 55 is 3.77 approximately.

Is the Cube Root of 55 Irrational?

Yes, because ∛55 = ∛(5 × 11) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 55 is an irrational number.

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Cube Root of 55 Solved Examples

Example 1: What is the value of ∛55 + ∛(-55)?

Solution:

The cube root of -55 is equal to the negative of the cube root of 55.
i.e. ∛-55 = -∛55

Therefore, ∛55 + ∛(-55) = ∛55 - ∛55 = 0
Example 2: The volume of a spherical ball is 55π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 55π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 55
⇒ R = ∛(3/4 × 55) = ∛(3/4) × ∛55 = 0.90856 × 3.80295 (∵ ∛(3/4) = 0.90856 and ∛55 = 3.80295)
⇒ R = 3.45521 in³
Example 3: Given the volume of a cube is 55 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 55 in³ = a³
⇒ a³ = 55
Cube rooting on both sides,
⇒ a = ∛55 in
Since the cube root of 55 is 3.8, therefore, the length of the side of the cube is 3.8 in.

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FAQs on Cube Root of 55

What is the Value of the Cube Root of 55?

We can express 55 as 5 × 11 i.e. ∛55 = ∛(5 × 11) = 3.80295. Therefore, the value of the cube root of 55 is 3.80295.

How to Simplify the Cube Root of 55/729?

We know that the cube root of 55 is 3.80295 and the cube root of 729 is 9. Therefore, ∛(55/729) = (∛55)/(∛729) = 3.803/9 = 0.4226.

What is the Cube Root of -55?

The cube root of -55 is equal to the negative of the cube root of 55. Therefore, ∛-55 = -(∛55) = -(3.803) = -3.803.

If the Cube Root of 55 is 3.8, Find the Value of ∛0.055.

Let us represent ∛0.055 in p/q form i.e. ∛(55/1000) = 3.8/10 = 0.38. Hence, the value of ∛0.055 = 0.38.

What is the Cube of the Cube Root of 55?

The cube of the cube root of 55 is the number 55 itself i.e. (∛55)³ = (55^1/3)³ = 55.

Why is the Value of the Cube Root of 55 Irrational?

The value of the cube root of 55 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛55 is irrational.