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Cube Root of 9

The value of the cube root of 9 rounded to 4 decimal places is 2.0801. It is the real solution of the equation x³ = 9. The cube root of 9 is expressed as ∛9 in the radical form and as (9)^⅓ or (9)^0.33 in the exponent form. The prime factorization of 9 is 3 × 3, hence, the cube root of 9 in its lowest radical form is expressed as ∛9.

Cube root of 9: 2.080083823
Cube root of 9 in Exponential Form: (9)^⅓
Cube root of 9 in Radical Form: ∛9

Cube Root of 9

1.	What is the Cube Root of 9?
2.	How to Calculate the Cube Root of 9?
3.	Is the Cube Root of 9 Irrational?
4.	FAQs on Cube Root of 9

What is the Cube Root of 9?

The cube root of 9 is the number which when multiplied by itself three times gives the product as 9. Since 9 can be expressed as 3 × 3. Therefore, the cube root of 9 = ∛(3 × 3) = 2.0801.

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How to Calculate the Value of the Cube Root of 9?

Cube Root of 9 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 = 9
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 9]
⇒ x = 2
Therefore,
∛9 = 2 (2³ + 2 × 9)/(2 × 2³ + 9)) = 2.08
⇒ ∛9 ≈ 2.08
Therefore, the cube root of 9 is 2.08 approximately.

Is the Cube Root of 9 Irrational?

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

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Cube Root of 9 Solved Examples

Example 1: Find the real root of the equation x³ − 9 = 0.

Solution:

x³ − 9 = 0 i.e. x³ = 9
Solving for x gives us,
x = ∛9, x = ∛9 × (-1 + √3i))/2 and x = ∛9 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛9
Therefore, the real root of the equation x³ − 9 = 0 is for x = ∛9 = 2.0801.
Example 2: What is the value of ∛9 + ∛(-9)?

Solution:

The cube root of -9 is equal to the negative of the cube root of 9.
i.e. ∛-9 = -∛9

Therefore, ∛9 + ∛(-9) = ∛9 - ∛9 = 0
Example 3: The volume of a spherical ball is 9π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 9π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 9
⇒ R = ∛(3/4 × 9) = ∛(3/4) × ∛9 = 0.90856 × 2.08008 (∵ ∛(3/4) = 0.90856 and ∛9 = 2.08008)
⇒ R = 1.88988 in³

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FAQs on Cube Root of 9

What is the Value of the Cube Root of 9?

We can express 9 as 3 × 3 i.e. ∛9 = ∛(3 × 3) = 2.08008. Therefore, the value of the cube root of 9 is 2.08008.

Why is the Value of the Cube Root of 9 Irrational?

The value of the cube root of 9 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛9 is irrational.

Is 9 a Perfect Cube?

The number 9 on prime factorization gives 3 × 3. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 9 is irrational, hence 9 is not a perfect cube.

What is the Cube Root of -9?

The cube root of -9 is equal to the negative of the cube root of 9. Therefore, ∛-9 = -(∛9) = -(2.08) = -2.08.

What is the Cube of the Cube Root of 9?

The cube of the cube root of 9 is the number 9 itself i.e. (∛9)³ = (9^1/3)³ = 9.

What is the Value of 4 Plus 8 Cube Root 9?

The value of ∛9 is 2.08. So, 4 + 8 × ∛9 = 4 + 8 × 2.08 = 20.64. Hence, the value of 4 plus 8 cube root 9 is 20.64.

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