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Cube Root of 9000

The value of the cube root of 9000 rounded to 4 decimal places is 20.8008. It is the real solution of the equation x³ = 9000. The cube root of 9000 is expressed as ∛9000 or 10 ∛9 in the radical form and as (9000)^⅓ or (9000)^0.33 in the exponent form. The prime factorization of 9000 is 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5, hence, the cube root of 9000 in its lowest radical form is expressed as 10 ∛9.

Cube root of 9000: 20.800838231
Cube root of 9000 in Exponential Form: (9000)^⅓
Cube root of 9000 in Radical Form: ∛9000 or 10 ∛9

Cube Root of 9000

1.	What is the Cube Root of 9000?
2.	How to Calculate the Cube Root of 9000?
3.	Is the Cube Root of 9000 Irrational?
4.	FAQs on Cube Root of 9000

What is the Cube Root of 9000?

The cube root of 9000 is the number which when multiplied by itself three times gives the product as 9000. Since 9000 can be expressed as 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5. Therefore, the cube root of 9000 = ∛(2 × 2 × 2 × 3 × 3 × 5 × 5 × 5) = 20.8008.

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How to Calculate the Value of the Cube Root of 9000?

Cube Root of 9000 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 = 9000
Let us assume x as 20
[∵ 20³ = 8000 and 8000 is the nearest perfect cube that is less than 9000]
⇒ x = 20
Therefore,
∛9000 = 20 (20³ + 2 × 9000)/(2 × 20³ + 9000)) = 20.8
⇒ ∛9000 ≈ 20.8
Therefore, the cube root of 9000 is 20.8 approximately.

Is the Cube Root of 9000 Irrational?

Yes, because ∛9000 = ∛(2 × 2 × 2 × 3 × 3 × 5 × 5 × 5) = 10 ∛9 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 9000 is an irrational number.

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Cube Root of 9000 Solved Examples

Example 1: What is the value of ∛9000 ÷ ∛(-9000)?

Solution:

The cube root of -9000 is equal to the negative of the cube root of 9000.
⇒ ∛-9000 = -∛9000

Therefore,
⇒ ∛9000/∛(-9000) = ∛9000/(-∛9000) = -1
Example 2: Given the volume of a cube is 9000 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 9000 in³ = a³
⇒ a³ = 9000
Cube rooting on both sides,
⇒ a = ∛9000 in
Since the cube root of 9000 is 20.8, therefore, the length of the side of the cube is 20.8 in.
Example 3: Find the real root of the equation x³ − 9000 = 0.

Solution:

x³ − 9000 = 0 i.e. x³ = 9000
Solving for x gives us,
x = ∛9000, x = ∛9000 × (-1 + √3i))/2 and x = ∛9000 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛9000
Therefore, the real root of the equation x³ − 9000 = 0 is for x = ∛9000 = 20.8008.

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FAQs on Cube Root of 9000

What is the Value of the Cube Root of 9000?

We can express 9000 as 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5 i.e. ∛9000 = ∛(2 × 2 × 2 × 3 × 3 × 5 × 5 × 5) = 20.80084. Therefore, the value of the cube root of 9000 is 20.80084.

How to Simplify the Cube Root of 9000/64?

We know that the cube root of 9000 is 20.80084 and the cube root of 64 is 4. Therefore, ∛(9000/64) = (∛9000)/(∛64) = 20.801/4 = 5.2002.

What is the Cube Root of -9000?

The cube root of -9000 is equal to the negative of the cube root of 9000. Therefore, ∛-9000 = -(∛9000) = -(20.801) = -20.801.

What is the Cube of the Cube Root of 9000?

The cube of the cube root of 9000 is the number 9000 itself i.e. (∛9000)³ = (9000^1/3)³ = 9000.

Why is the Value of the Cube Root of 9000 Irrational?

The value of the cube root of 9000 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛9000 is irrational.

If the Cube Root of 9000 is 20.8, Find the Value of ∛9.

Let us represent ∛9.0 in p/q form i.e. ∛(9000/1000) = 20.8/10 = 2.08. Hence, the value of ∛9.0 = 2.08.

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