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Cube Root of 8000

The value of the cube root of 8000 is 20. It is the real solution of the equation x³ = 8000. The cube root of 8000 is expressed as ∛8000 in radical form and as (8000)^⅓ or (8000)^0.33 in the exponent form. As the cube root of 8000 is a whole number, 8000 is a perfect cube.

Cube root of 8000: 20
Cube root of 8000 in exponential form: (8000)^⅓
Cube root of 8000 in radical form: ∛8000

Cube Root of 8000

1.	What is the Cube Root of 8000?
2.	How to Calculate the Cube Root of 8000?
3.	Is the Cube Root of 8000 Irrational?
4.	FAQs on Cube Root of 8000

What is the Cube Root of 8000?

The cube root of 8000 is the number which when multiplied by itself three times gives the product as 8000. Since 8000 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5. Therefore, the cube root of 8000 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5) = 20.

How to Calculate the Value of the Cube Root of 8000?

Cube Root of 8000 by Prime Factorization

Prime factorization of 8000 is 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5
Simplifying the above expression: 2⁶ × 5³
Simplifying further: 20³

Therefore, the cube root of 8000 by prime factorization is (2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5)^1/3 = 20.

Is the Cube Root of 8000 Irrational?

No, because ∛8000 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5) can be expressed in the form of p/q i.e. 20/1. Therefore, the value of the cube root of 8000 is an integer (rational).

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Cube Root of 8000 Solved Examples

Example 1: Given the volume of a cube is 8000 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 8000 in³ = a³
⇒ a³ = 8000
Cube rooting on both sides,
⇒ a = ∛8000 in
Since the cube root of 8000 is 20, therefore, the length of the side of the cube is 20 in.
Example 2: The volume of a spherical ball is 8000π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 8000π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 8000
⇒ R = ∛(3/4 × 8000) = ∛(3/4) × ∛8000 = 0.90856 × 20 (∵ ∛(3/4) = 0.90856 and ∛8000 = 20)
⇒ R = 18.1712 in³
Example 3: Find the real root of the equation x³ − 8000 = 0.

Solution:

x³ − 8000 = 0 i.e. x³ = 8000
Solving for x gives us,
x = ∛8000, x = ∛8000 × (-1 + √3i))/2 and x = ∛8000 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛8000
Therefore, the real root of the equation x³ − 8000 = 0 is for x = ∛8000 = 20.

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FAQs on Cube Root of 8000

What is the Value of the Cube Root of 8000?

We can express 8000 as 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 i.e. ∛8000 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5) = 20. Therefore, the value of the cube root of 8000 is 20.

What is the Value of 10 Plus 1 Cube Root 8000?

The value of ∛8000 is 20. So, 10 + 1 × ∛8000 = 10 + 1 × 20 = 30. Hence, the value of 10 plus 1 cube root 8000 is 30.

What is the Cube Root of -8000?

The cube root of -8000 is equal to the negative of the cube root of 8000. Therefore, ∛-8000 = -(∛8000) = -(20) = -20.

If the Cube Root of 8000 is 20, Find the Value of ∛8.

Let us represent ∛8 in p/q form i.e. ∛(8000/1000) = 20/10 = 2. Hence, the value of ∛8 = 2.

Why is the value of the Cube Root of 8000 Rational?

The value of the cube root of 8000 can be expressed in the form of p/q i.e. = 20/1, where q ≠ 0. Therefore, the ∛8000 is rational.

Is 8000 a Perfect Cube?

The number 8000 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5. On combining the prime factors in groups of 3 gives 20. So, the cube root of 8000 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5) = 20 (perfect cube).

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