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Cube Root of 23

The value of the cube root of 23 rounded to 5 decimal places is 2.84387. It is the real solution of the equation x3 = 23. The cube root of 23 is expressed as ∛23 in the radical form and as (23)⅓ or (23)0.33 in the exponent form. The prime factorization of 23 is 23, hence, the cube root of 23 in its lowest radical form is expressed as ∛23.

  • Cube root of 23: 2.84386698
  • Cube root of 23 in Exponential Form: (23)⅓
  • Cube root of 23 in Radical Form: ∛23

Cube Root of 23

1. What is the Cube Root of 23?
2. How to Calculate the Cube Root of 23?
3. Is the Cube Root of 23 Irrational?
4. FAQs on Cube Root of 23

What is the Cube Root of 23?

The cube root of 23 is the number which when multiplied by itself three times gives the product as 23. The number 23 is prime. Therefore, the cube root of 23 = ∛23 = 2.8439.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 23?

Cube Root of 23 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 = 23
Let us assume x as 2
[∵ 23 = 8 and 8 is the nearest perfect cube that is less than 23]
⇒ x = 2
Therefore,
∛23 = 2 (23 + 2 × 23)/(2 × 23 + 23)) = 2.77
⇒ ∛23 ≈ 2.77
Therefore, the cube root of 23 is 2.77 approximately.

Is the Cube Root of 23 Irrational?

Yes, because ∛23 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 23 is an irrational number.

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Cube Root of 23 Solved Examples

  1. Example 1: What is the value of ∛23 + ∛(-23)?

    Solution:

    The cube root of -23 is equal to the negative of the cube root of 23.
    i.e. ∛-23 = -∛23

    Therefore, ∛23 + ∛(-23) = ∛23 - ∛23 = 0

  2. Example 2: The volume of a spherical ball is 23π in3. What is the radius of this ball?

    Solution:

    Volume of the spherical ball = 23π in3
    = 4/3 × π × R3
    ⇒ R3 = 3/4 × 23
    ⇒ R = ∛(3/4 × 23) = ∛(3/4) × ∛23 = 0.90856 × 2.84387 (∵ ∛(3/4) = 0.90856 and ∛23 = 2.84387)
    ⇒ R = 2.58383 in3

  3. Example 3: Find the real root of the equation x3 − 23 = 0.

    Solution:

    x3 − 23 = 0 i.e. x3 = 23
    Solving for x gives us,
    x = ∛23, x = ∛23 × (-1 + √3i))/2 and x = ∛23 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛23
    Therefore, the real root of the equation x3 − 23 = 0 is for x = ∛23 = 2.8439.

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FAQs on Cube Root of 23

What is the Value of the Cube Root of 23?

The value of the cube root of 23 is 2.84387.

Why is the Value of the Cube Root of 23 Irrational?

The value of the cube root of 23 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛23 is irrational.

What is the Cube Root of -23?

The cube root of -23 is equal to the negative of the cube root of 23. Therefore, ∛-23 = -(∛23) = -(2.844) = -2.844.

What is the Cube of the Cube Root of 23?

The cube of the cube root of 23 is the number 23 itself i.e. (∛23)3 = (231/3)3 = 23.

Is 23 a Perfect Cube?

The number 23 is prime. Here, the prime factor 23 is not in the power of 3 and this implies that the cube root of 23 is irrational, hence 23 is not a perfect cube.

If the Cube Root of 23 is 2.84, Find the Value of ∛0.023.

Let us represent ∛0.023 in p/q form i.e. ∛(23/1000) = 2.84/10 = 0.28. Hence, the value of ∛0.023 = 0.28.

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