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Cube Root of 128

The value of the cube root of 128 rounded to 6 decimal places is 5.039684. It is the real solution of the equation x³ = 128. The cube root of 128 is expressed as ∛128 or 4 ∛2 in the radical form and as (128)^⅓ or (128)^0.33 in the exponent form. The prime factorization of 128 is 2 × 2 × 2 × 2 × 2 × 2 × 2, hence, the cube root of 128 in its lowest radical form is expressed as 4 ∛2.

Cube root of 128: 5.0396842
Cube root of 128 in Exponential Form: (128)^⅓
Cube root of 128 in Radical Form: ∛128 or 4 ∛2

1.	What is the Cube Root of 128?
2.	How to Calculate the Cube Root of 128?
3.	Is the Cube Root of 128 Irrational?
4.	FAQs on Cube Root of 128

What is the Cube Root of 128?

The cube root of 128 is the number which when multiplied by itself three times gives the product as 128. Since 128 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 2. Therefore, the cube root of 128 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2) = 5.0397.

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How to Calculate the Value of the Cube Root of 128?

Cube Root of 128 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 = 128
Let us assume x as 5
[∵ 5³ = 125 and 125 is the nearest perfect cube that is less than 128]
⇒ x = 5
Therefore,
∛128 = 5 (5³ + 2 × 128)/(2 × 5³ + 128)) = 5.04
⇒ ∛128 ≈ 5.04
Therefore, the cube root of 128 is 5.04 approximately.

Is the Cube Root of 128 Irrational?

Yes, because ∛128 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2) = 4 ∛2 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 128 is an irrational number.

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Cube Root of 128 Solved Examples

Example 1: What is the value of ∛128 + ∛(-128)?

Solution:

The cube root of -128 is equal to the negative of the cube root of 128.
i.e. ∛-128 = -∛128

Therefore, ∛128 + ∛(-128) = ∛128 - ∛128 = 0
Example 2: Given the volume of a cube is 128 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 128 in³ = a³
⇒ a³ = 128
Cube rooting on both sides,
⇒ a = ∛128 in
Since the cube root of 128 is 5.04, therefore, the length of the side of the cube is 5.04 in.
Example 3: The volume of a spherical ball is 128π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 128π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 128
⇒ R = ∛(3/4 × 128) = ∛(3/4) × ∛128 = 0.90856 × 5.03968 (∵ ∛(3/4) = 0.90856 and ∛128 = 5.03968)
⇒ R = 4.57885 in³

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FAQs on Cube Root of 128

What is the Value of the Cube Root of 128?

We can express 128 as 2 × 2 × 2 × 2 × 2 × 2 × 2 i.e. ∛128 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2) = 5.03968. Therefore, the value of the cube root of 128 is 5.03968.

How to Simplify the Cube Root of 128/343?

We know that the cube root of 128 is 5.03968 and the cube root of 343 is 7. Therefore, ∛(128/343) = (∛128)/(∛343) = 5.04/7 = 0.72.

If the Cube Root of 128 is 5.04, Find the Value of ∛0.128.

Let us represent ∛0.128 in p/q form i.e. ∛(128/1000) = 5.04/10 = 0.5. Hence, the value of ∛0.128 = 0.5.

What is the Value of 17 Plus 1 Cube Root 128?

The value of ∛128 is 5.04. So, 17 + 1 × ∛128 = 17 + 1 × 5.04 = 22.04. Hence, the value of 17 plus 1 cube root 128 is 22.04.

What is the Cube Root of -128?

The cube root of -128 is equal to the negative of the cube root of 128. Therefore, ∛-128 = -(∛128) = -(5.04) = -5.04.

Is 128 a Perfect Cube?

The number 128 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 2 × 2. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 128 is irrational, hence 128 is not a perfect cube.