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Cube Root of 80

The value of the cube root of 80 rounded to 4 decimal places is 4.3089. It is the real solution of the equation x³ = 80. The cube root of 80 is expressed as ∛80 or 2 ∛10 in the radical form and as (80)^⅓ or (80)^0.33 in the exponent form. The prime factorization of 80 is 2 × 2 × 2 × 2 × 5, hence, the cube root of 80 in its lowest radical form is expressed as 2 ∛10.

Cube root of 80: 4.30886938
Cube root of 80 in Exponential Form: (80)^⅓
Cube root of 80 in Radical Form: ∛80 or 2 ∛10

Cube Root of 80

1.	What is the Cube Root of 80?
2.	How to Calculate the Cube Root of 80?
3.	Is the Cube Root of 80 Irrational?
4.	FAQs on Cube Root of 80

What is the Cube Root of 80?

The cube root of 80 is the number which when multiplied by itself three times gives the product as 80. Since 80 can be expressed as 2 × 2 × 2 × 2 × 5. Therefore, the cube root of 80 = ∛(2 × 2 × 2 × 2 × 5) = 4.3089.

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How to Calculate the Value of the Cube Root of 80?

Cube Root of 80 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 = 80
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 80]
⇒ x = 4
Therefore,
∛80 = 4 (4³ + 2 × 80)/(2 × 4³ + 80)) = 4.31
⇒ ∛80 ≈ 4.31
Therefore, the cube root of 80 is 4.31 approximately.

Is the Cube Root of 80 Irrational?

Yes, because ∛80 = ∛(2 × 2 × 2 × 2 × 5) = 2 ∛10 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 80 is an irrational number.

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Cube Root of 80 Solved Examples

Example 1: What is the value of ∛80 + ∛(-80)?

Solution:

The cube root of -80 is equal to the negative of the cube root of 80.
i.e. ∛-80 = -∛80

Therefore, ∛80 + ∛(-80) = ∛80 - ∛80 = 0
Example 2: The volume of a spherical ball is 80π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 80π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 80
⇒ R = ∛(3/4 × 80) = ∛(3/4) × ∛80 = 0.90856 × 4.30887 (∵ ∛(3/4) = 0.90856 and ∛80 = 4.30887)
⇒ R = 3.91487 in³
Example 3: Find the real root of the equation x³ − 80 = 0.

Solution:

x³ − 80 = 0 i.e. x³ = 80
Solving for x gives us,
x = ∛80, x = ∛80 × (-1 + √3i))/2 and x = ∛80 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛80
Therefore, the real root of the equation x³ − 80 = 0 is for x = ∛80 = 4.3089.

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FAQs on Cube Root of 80

What is the Value of the Cube Root of 80?

We can express 80 as 2 × 2 × 2 × 2 × 5 i.e. ∛80 = ∛(2 × 2 × 2 × 2 × 5) = 4.30887. Therefore, the value of the cube root of 80 is 4.30887.

Why is the Value of the Cube Root of 80 Irrational?

The value of the cube root of 80 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛80 is irrational.

If the Cube Root of 80 is 4.31, Find the Value of ∛0.08.

Let us represent ∛0.08 in p/q form i.e. ∛(80/1000) = 4.31/10 = 0.43. Hence, the value of ∛0.08 = 0.43.

Is 80 a Perfect Cube?

The number 80 on prime factorization gives 2 × 2 × 2 × 2 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 80 is irrational, hence 80 is not a perfect cube.

What is the Cube Root of -80?

The cube root of -80 is equal to the negative of the cube root of 80. Therefore, ∛-80 = -(∛80) = -(4.309) = -4.309.

How to Simplify the Cube Root of 80/216?

We know that the cube root of 80 is 4.30887 and the cube root of 216 is 6. Therefore, ∛(80/216) = (∛80)/(∛216) = 4.309/6 = 0.7182.

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