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Cube Root of 47

The value of the cube root of 47 rounded to 6 decimal places is 3.608826. It is the real solution of the equation x3 = 47. The cube root of 47 is expressed as ∛47 in the radical form and as (47)⅓ or (47)0.33 in the exponent form. The prime factorization of 47 is 47, hence, the cube root of 47 in its lowest radical form is expressed as ∛47.

  • Cube root of 47: 3.60882608
  • Cube root of 47 in Exponential Form: (47)⅓
  • Cube root of 47 in Radical Form: ∛47

Cube Root of 47

1. What is the Cube Root of 47?
2. How to Calculate the Cube Root of 47?
3. Is the Cube Root of 47 Irrational?
4. FAQs on Cube Root of 47

What is the Cube Root of 47?

The cube root of 47 is the number which when multiplied by itself three times gives the product as 47. The number 47 is prime. Therefore, the cube root of 47 = ∛47 = 3.6088.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 47?

Cube Root of 47 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 = 47
Let us assume x as 3
[∵ 33 = 27 and 27 is the nearest perfect cube that is less than 47]
⇒ x = 3
Therefore,
∛47 = 3 (33 + 2 × 47)/(2 × 33 + 47)) = 3.59
⇒ ∛47 ≈ 3.59
Therefore, the cube root of 47 is 3.59 approximately.

Is the Cube Root of 47 Irrational?

Yes, because ∛47 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 47 is an irrational number.

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Cube Root of 47 Solved Examples

  1. Example 1: Find the real root of the equation x3 − 47 = 0.

    Solution:

    x3 − 47 = 0 i.e. x3 = 47
    Solving for x gives us,
    x = ∛47, x = ∛47 × (-1 + √3i))/2 and x = ∛47 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛47
    Therefore, the real root of the equation x3 − 47 = 0 is for x = ∛47 = 3.6088.

  2. Example 2: The volume of a spherical ball is 47π in3. What is the radius of this ball?

    Solution:

    Volume of the spherical ball = 47π in3
    = 4/3 × π × R3
    ⇒ R3 = 3/4 × 47
    ⇒ R = ∛(3/4 × 47) = ∛(3/4) × ∛47 = 0.90856 × 3.60883 (∵ ∛(3/4) = 0.90856 and ∛47 = 3.60883)
    ⇒ R = 3.27884 in3

  3. Example 3: What is the value of ∛47 + ∛(-47)?

    Solution:

    The cube root of -47 is equal to the negative of the cube root of 47.
    i.e. ∛-47 = -∛47

    Therefore, ∛47 + ∛(-47) = ∛47 - ∛47 = 0

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FAQs on Cube Root of 47

What is the Value of the Cube Root of 47?

The value of the cube root of 47 is 3.60883.

Why is the Value of the Cube Root of 47 Irrational?

The value of the cube root of 47 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛47 is irrational.

What is the Value of 4 Plus 3 Cube Root 47?

The value of ∛47 is 3.609. So, 4 + 3 × ∛47 = 4 + 3 × 3.609 = 14.827. Hence, the value of 4 plus 3 cube root 47 is 14.827.

What is the Cube of the Cube Root of 47?

The cube of the cube root of 47 is the number 47 itself i.e. (∛47)3 = (471/3)3 = 47.

Is 47 a Perfect Cube?

The number 47 is prime. Here, the prime factor 47 is not in the power of 3 and this implies that the cube root of 47 is irrational, hence 47 is not a perfect cube.

If the Cube Root of 47 is 3.61, Find the Value of ∛0.047.

Let us represent ∛0.047 in p/q form i.e. ∛(47/1000) = 3.61/10 = 0.36. Hence, the value of ∛0.047 = 0.36.

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