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Cube Root of 43

The value of the cube root of 43 rounded to 4 decimal places is 3.5034. It is the real solution of the equation x3 = 43. The cube root of 43 is expressed as ∛43 in the radical form and as (43)⅓ or (43)0.33 in the exponent form. The prime factorization of 43 is 43, hence, the cube root of 43 in its lowest radical form is expressed as ∛43.

  • Cube root of 43: 3.50339806
  • Cube root of 43 in Exponential Form: (43)⅓
  • Cube root of 43 in Radical Form: ∛43

Cube Root of 43

1. What is the Cube Root of 43?
2. How to Calculate the Cube Root of 43?
3. Is the Cube Root of 43 Irrational?
4. FAQs on Cube Root of 43

What is the Cube Root of 43?

The cube root of 43 is the number which when multiplied by itself three times gives the product as 43. The number 43 is prime. Therefore, the cube root of 43 = ∛43 = 3.5034.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 43?

Cube Root of 43 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 = 43
Let us assume x as 3
[∵ 33 = 27 and 27 is the nearest perfect cube that is less than 43]
⇒ x = 3
Therefore,
∛43 = 3 (33 + 2 × 43)/(2 × 33 + 43)) = 3.49
⇒ ∛43 ≈ 3.49
Therefore, the cube root of 43 is 3.49 approximately.

Is the Cube Root of 43 Irrational?

Yes, because ∛43 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 43 is an irrational number.

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Cube Root of 43 Solved Examples

  1. Example 1: Given the volume of a cube is 43 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 43 in3 = a3
    ⇒ a3 = 43
    Cube rooting on both sides,
    ⇒ a = ∛43 in
    Since the cube root of 43 is 3.5, therefore, the length of the side of the cube is 3.5 in.

  2. Example 2: Find the real root of the equation x3 − 43 = 0.

    Solution:

    x3 − 43 = 0 i.e. x3 = 43
    Solving for x gives us,
    x = ∛43, x = ∛43 × (-1 + √3i))/2 and x = ∛43 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛43
    Therefore, the real root of the equation x3 − 43 = 0 is for x = ∛43 = 3.5034.

  3. Example 3: The volume of a spherical ball is 43π in3. What is the radius of this ball?

    Solution:

    Volume of the spherical ball = 43π in3
    = 4/3 × π × R3
    ⇒ R3 = 3/4 × 43
    ⇒ R = ∛(3/4 × 43) = ∛(3/4) × ∛43 = 0.90856 × 3.5034 (∵ ∛(3/4) = 0.90856 and ∛43 = 3.5034)
    ⇒ R = 3.18305 in3

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FAQs on Cube Root of 43

What is the Value of the Cube Root of 43?

The value of the cube root of 43 is 3.5034.

What is the Cube of the Cube Root of 43?

The cube of the cube root of 43 is the number 43 itself i.e. (∛43)3 = (431/3)3 = 43.

Is 43 a Perfect Cube?

The number 43 is prime. Here, the prime factor 43 is not in the power of 3 and this implies that the cube root of 43 is irrational, hence 43 is not a perfect cube.

How to Simplify the Cube Root of 43/64?

We know that the cube root of 43 is 3.5034 and the cube root of 64 is 4. Therefore, ∛(43/64) = (∛43)/(∛64) = 3.503/4 = 0.8758.

What is the Value of 4 Plus 12 Cube Root 43?

The value of ∛43 is 3.503. So, 4 + 12 × ∛43 = 4 + 12 × 3.503 = 46.036. Hence, the value of 4 plus 12 cube root 43 is 46.036.

Why is the Value of the Cube Root of 43 Irrational?

The value of the cube root of 43 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛43 is irrational.

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