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Cube Root of 87

The value of the cube root of 87 rounded to 5 decimal places is 4.43105. It is the real solution of the equation x3 = 87. The cube root of 87 is expressed as ∛87 in the radical form and as (87)⅓ or (87)0.33 in the exponent form. The prime factorization of 87 is 3 × 29, hence, the cube root of 87 in its lowest radical form is expressed as ∛87.

  • Cube root of 87: 4.431047622
  • Cube root of 87 in Exponential Form: (87)⅓
  • Cube root of 87 in Radical Form: ∛87

Cube Root of 87

1. What is the Cube Root of 87?
2. How to Calculate the Cube Root of 87?
3. Is the Cube Root of 87 Irrational?
4. FAQs on Cube Root of 87

What is the Cube Root of 87?

The cube root of 87 is the number which when multiplied by itself three times gives the product as 87. Since 87 can be expressed as 3 × 29. Therefore, the cube root of 87 = ∛(3 × 29) = 4.431.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 87?

Cube Root of 87 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 = 87
Let us assume x as 4
[∵ 43 = 64 and 64 is the nearest perfect cube that is less than 87]
⇒ x = 4
Therefore,
∛87 = 4 (43 + 2 × 87)/(2 × 43 + 87)) = 4.43
⇒ ∛87 ≈ 4.43
Therefore, the cube root of 87 is 4.43 approximately.

Is the Cube Root of 87 Irrational?

Yes, because ∛87 = ∛(3 × 29) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 87 is an irrational number.

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Cube Root of 87 Solved Examples

  1. Example 1: Find the real root of the equation x3 − 87 = 0.

    Solution:

    x3 − 87 = 0 i.e. x3 = 87
    Solving for x gives us,
    x = ∛87, x = ∛87 × (-1 + √3i))/2 and x = ∛87 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛87
    Therefore, the real root of the equation x3 − 87 = 0 is for x = ∛87 = 4.431.

  2. Example 2: What is the value of ∛87 + ∛(-87)?

    Solution:

    The cube root of -87 is equal to the negative of the cube root of 87.
    i.e. ∛-87 = -∛87

    Therefore, ∛87 + ∛(-87) = ∛87 - ∛87 = 0

  3. Example 3: The volume of a spherical ball is 87π in3. What is the radius of this ball?

    Solution:

    Volume of the spherical ball = 87π in3
    = 4/3 × π × R3
    ⇒ R3 = 3/4 × 87
    ⇒ R = ∛(3/4 × 87) = ∛(3/4) × ∛87 = 0.90856 × 4.43105 (∵ ∛(3/4) = 0.90856 and ∛87 = 4.43105)
    ⇒ R = 4.02587 in3

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FAQs on Cube Root of 87

What is the Value of the Cube Root of 87?

We can express 87 as 3 × 29 i.e. ∛87 = ∛(3 × 29) = 4.43105. Therefore, the value of the cube root of 87 is 4.43105.

What is the Cube Root of -87?

The cube root of -87 is equal to the negative of the cube root of 87. Therefore, ∛-87 = -(∛87) = -(4.431) = -4.431.

How to Simplify the Cube Root of 87/216?

We know that the cube root of 87 is 4.43105 and the cube root of 216 is 6. Therefore, ∛(87/216) = (∛87)/(∛216) = 4.431/6 = 0.7385.

Why is the Value of the Cube Root of 87 Irrational?

The value of the cube root of 87 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛87 is irrational.

What is the Cube of the Cube Root of 87?

The cube of the cube root of 87 is the number 87 itself i.e. (∛87)3 = (871/3)3 = 87.

What is the Value of 7 Plus 2 Cube Root 87?

The value of ∛87 is 4.431. So, 7 + 2 × ∛87 = 7 + 2 × 4.431 = 15.862. Hence, the value of 7 plus 2 cube root 87 is 15.862.

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