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Cube Root of 54

The value of the cube root of 54 rounded to 7 decimal places is 3.7797631. It is the real solution of the equation x³ = 54. The cube root of 54 is expressed as ∛54 or 3 ∛2 in the radical form and as (54)^⅓ or (54)^0.33 in the exponent form. The prime factorization of 54 is 2 × 3 × 3 × 3, hence, the cube root of 54 in its lowest radical form is expressed as 3 ∛2.

Cube root of 54: 3.77976315
Cube root of 54 in Exponential Form: (54)^⅓
Cube root of 54 in Radical Form: ∛54 or 3 ∛2

1.	What is the Cube Root of 54?
2.	How to Calculate the Cube Root of 54?
3.	Is the Cube Root of 54 Irrational?
4.	FAQs on Cube Root of 54

What is the Cube Root of 54?

The cube root of 54 is the number which when multiplied by itself three times gives the product as 54. Since 54 can be expressed as 2 × 3 × 3 × 3. Therefore, the cube root of 54 = ∛(2 × 3 × 3 × 3) = 3.7798.

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How to Calculate the Value of the Cube Root of 54?

Cube Root of 54 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 = 54
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 54]
⇒ x = 3
Therefore,
∛54 = 3 (3³ + 2 × 54)/(2 × 3³ + 54)) = 3.75
⇒ ∛54 ≈ 3.75
Therefore, the cube root of 54 is 3.75 approximately.

Is the Cube Root of 54 Irrational?

Yes, because ∛54 = ∛(2 × 3 × 3 × 3) = 3 ∛2 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 54 is an irrational number.

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Cube Root of 54 Solved Examples

Example 1: What is the value of ∛54 + ∛(-54)?

Solution:

The cube root of -54 is equal to the negative of the cube root of 54.
i.e. ∛-54 = -∛54

Therefore, ∛54 + ∛(-54) = ∛54 - ∛54 = 0
Example 2: The volume of a spherical ball is 54π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 54π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 54
⇒ R = ∛(3/4 × 54) = ∛(3/4) × ∛54 = 0.90856 × 3.77976 (∵ ∛(3/4) = 0.90856 and ∛54 = 3.77976)
⇒ R = 3.43414 in³
Example 3: Given the volume of a cube is 54 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 54 in³ = a³
⇒ a³ = 54
Cube rooting on both sides,
⇒ a = ∛54 in
Since the cube root of 54 is 3.78, therefore, the length of the side of the cube is 3.78 in.

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FAQs on Cube Root of 54

What is the Value of the Cube Root of 54?

We can express 54 as 2 × 3 × 3 × 3 i.e. ∛54 = ∛(2 × 3 × 3 × 3) = 3.77976. Therefore, the value of the cube root of 54 is 3.77976.

What is the Cube of the Cube Root of 54?

The cube of the cube root of 54 is the number 54 itself i.e. (∛54)³ = (54^1/3)³ = 54.

Why is the Value of the Cube Root of 54 Irrational?

The value of the cube root of 54 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛54 is irrational.

What is the Value of 5 Plus 4 Cube Root 54?

The value of ∛54 is 3.78. So, 5 + 4 × ∛54 = 5 + 4 × 3.78 = 20.119999999999997. Hence, the value of 5 plus 4 cube root 54 is 20.119999999999997.

Is 54 a Perfect Cube?

The number 54 on prime factorization gives 2 × 3 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 54 is irrational, hence 54 is not a perfect cube.

What is the Cube Root of -54?

The cube root of -54 is equal to the negative of the cube root of 54. Therefore, ∛-54 = -(∛54) = -(3.78) = -3.78.