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Cube Root of 28

The value of the cube root of 28 rounded to 6 decimal places is 3.036589. It is the real solution of the equation x³ = 28. The cube root of 28 is expressed as ∛28 in the radical form and as (28)^⅓ or (28)^0.33 in the exponent form. The prime factorization of 28 is 2 × 2 × 7, hence, the cube root of 28 in its lowest radical form is expressed as ∛28.

Cube root of 28: 3.036588972
Cube root of 28 in Exponential Form: (28)^⅓
Cube root of 28 in Radical Form: ∛28

1.	What is the Cube Root of 28?
2.	How to Calculate the Cube Root of 28?
3.	Is the Cube Root of 28 Irrational?
4.	FAQs on Cube Root of 28

What is the Cube Root of 28?

The cube root of 28 is the number which when multiplied by itself three times gives the product as 28. Since 28 can be expressed as 2 × 2 × 7. Therefore, the cube root of 28 = ∛(2 × 2 × 7) = 3.0366.

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How to Calculate the Value of the Cube Root of 28?

Cube Root of 28 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 = 28
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 28]
⇒ x = 3
Therefore,
∛28 = 3 (3³ + 2 × 28)/(2 × 3³ + 28)) = 3.04
⇒ ∛28 ≈ 3.04
Therefore, the cube root of 28 is 3.04 approximately.

Is the Cube Root of 28 Irrational?

Yes, because ∛28 = ∛(2 × 2 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 28 is an irrational number.

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Cube Root of 28 Solved Examples

Example 1: Given the volume of a cube is 28 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 28 in³ = a³
⇒ a³ = 28
Cube rooting on both sides,
⇒ a = ∛28 in
Since the cube root of 28 is 3.04, therefore, the length of the side of the cube is 3.04 in.
Example 2: What is the value of ∛28 ÷ ∛(-28)?

Solution:

The cube root of -28 is equal to the negative of the cube root of 28.
⇒ ∛-28 = -∛28

Therefore,
⇒ ∛28/∛(-28) = ∛28/(-∛28) = -1
Example 3: The volume of a spherical ball is 28π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 28π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 28
⇒ R = ∛(3/4 × 28) = ∛(3/4) × ∛28 = 0.90856 × 3.03659 (∵ ∛(3/4) = 0.90856 and ∛28 = 3.03659)
⇒ R = 2.75892 in³

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FAQs on Cube Root of 28

What is the Value of the Cube Root of 28?

We can express 28 as 2 × 2 × 7 i.e. ∛28 = ∛(2 × 2 × 7) = 3.03659. Therefore, the value of the cube root of 28 is 3.03659.

If the Cube Root of 28 is 3.04, Find the Value of ∛0.028.

Let us represent ∛0.028 in p/q form i.e. ∛(28/1000) = 3.04/10 = 0.3. Hence, the value of ∛0.028 = 0.3.

Is 28 a Perfect Cube?

The number 28 on prime factorization gives 2 × 2 × 7. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 28 is irrational, hence 28 is not a perfect cube.

Why is the Value of the Cube Root of 28 Irrational?

The value of the cube root of 28 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛28 is irrational.

What is the Cube of the Cube Root of 28?

The cube of the cube root of 28 is the number 28 itself i.e. (∛28)³ = (28^1/3)³ = 28.

What is the Cube Root of -28?

The cube root of -28 is equal to the negative of the cube root of 28. Therefore, ∛-28 = -(∛28) = -(3.037) = -3.037.