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Cube Root of 13

The value of the cube root of 13 rounded to 7 decimal places is 2.3513347. It is the real solution of the equation x3 = 13. The cube root of 13 is expressed as ∛13 in the radical form and as (13)⅓ or (13)0.33 in the exponent form. The prime factorization of 13 is 13, hence, the cube root of 13 in its lowest radical form is expressed as ∛13.

  • Cube root of 13: 2.351334688
  • Cube root of 13 in Exponential Form: (13)⅓
  • Cube root of 13 in Radical Form: ∛13

Cube Root of 13

1. What is the Cube Root of 13?
2. How to Calculate the Cube Root of 13?
3. Is the Cube Root of 13 Irrational?
4. FAQs on Cube Root of 13

What is the Cube Root of 13?

The cube root of 13 is the number which when multiplied by itself three times gives the product as 13. The number 13 is prime. Therefore, the cube root of 13 = ∛13 = 2.3513.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 13?

Cube Root of 13 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 = 13
Let us assume x as 2
[∵ 23 = 8 and 8 is the nearest perfect cube that is less than 13]
⇒ x = 2
Therefore,
∛13 = 2 (23 + 2 × 13)/(2 × 23 + 13)) = 2.34
⇒ ∛13 ≈ 2.34
Therefore, the cube root of 13 is 2.34 approximately.

Is the Cube Root of 13 Irrational?

Yes, because ∛13 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 13 is an irrational number.

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Cube Root of 13 Solved Examples

  1. Example 1: Find the real root of the equation x3 − 13 = 0.

    Solution:

    x3 − 13 = 0 i.e. x3 = 13
    Solving for x gives us,
    x = ∛13, x = ∛13 × (-1 + √3i))/2 and x = ∛13 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛13
    Therefore, the real root of the equation x3 − 13 = 0 is for x = ∛13 = 2.3513.

  2. Example 2: Given the volume of a cube is 13 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 13 in3 = a3
    ⇒ a3 = 13
    Cube rooting on both sides,
    ⇒ a = ∛13 in
    Since the cube root of 13 is 2.35, therefore, the length of the side of the cube is 2.35 in.

  3. Example 3: The volume of a spherical ball is 13π in3. What is the radius of this ball?

    Solution:

    Volume of the spherical ball = 13π in3
    = 4/3 × π × R3
    ⇒ R3 = 3/4 × 13
    ⇒ R = ∛(3/4 × 13) = ∛(3/4) × ∛13 = 0.90856 × 2.35133 (∵ ∛(3/4) = 0.90856 and ∛13 = 2.35133)
    ⇒ R = 2.13632 in3

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FAQs on Cube Root of 13

What is the Value of the Cube Root of 13?

The value of the cube root of 13 is 2.35133.

How to Simplify the Cube Root of 13/64?

We know that the cube root of 13 is 2.35133 and the cube root of 64 is 4. Therefore, ∛(13/64) = (∛13)/(∛64) = 2.351/4 = 0.5877.

What is the Value of 7 Plus 16 Cube Root 13?

The value of ∛13 is 2.351. So, 7 + 16 × ∛13 = 7 + 16 × 2.351 = 44.616. Hence, the value of 7 plus 16 cube root 13 is 44.616.

If the Cube Root of 13 is 2.35, Find the Value of ∛0.013.

Let us represent ∛0.013 in p/q form i.e. ∛(13/1000) = 2.35/10 = 0.24. Hence, the value of ∛0.013 = 0.24.

Why is the Value of the Cube Root of 13 Irrational?

The value of the cube root of 13 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛13 is irrational.

What is the Cube Root of -13?

The cube root of -13 is equal to the negative of the cube root of 13. Therefore, ∛-13 = -(∛13) = -(2.351) = -2.351.

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