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Cube Root of 99

The value of the cube root of 99 rounded to 5 decimal places is 4.62607. It is the real solution of the equation x³ = 99. The cube root of 99 is expressed as ∛99 in the radical form and as (99)^⅓ or (99)^0.33 in the exponent form. The prime factorization of 99 is 3 × 3 × 11, hence, the cube root of 99 in its lowest radical form is expressed as ∛99.

Cube root of 99: 4.626065009
Cube root of 99 in Exponential Form: (99)^⅓
Cube root of 99 in Radical Form: ∛99

1.	What is the Cube Root of 99?
2.	How to Calculate the Cube Root of 99?
3.	Is the Cube Root of 99 Irrational?
4.	FAQs on Cube Root of 99

What is the Cube Root of 99?

The cube root of 99 is the number which when multiplied by itself three times gives the product as 99. Since 99 can be expressed as 3 × 3 × 11. Therefore, the cube root of 99 = ∛(3 × 3 × 11) = 4.6261.

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How to Calculate the Value of the Cube Root of 99?

Cube Root of 99 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 = 99
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 99]
⇒ x = 4
Therefore,
∛99 = 4 (4³ + 2 × 99)/(2 × 4³ + 99)) = 4.62
⇒ ∛99 ≈ 4.62
Therefore, the cube root of 99 is 4.62 approximately.

Is the Cube Root of 99 Irrational?

Yes, because ∛99 = ∛(3 × 3 × 11) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 99 is an irrational number.

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Cube Root of 99 Solved Examples

Example 1: Given the volume of a cube is 99 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 99 in³ = a³
⇒ a³ = 99
Cube rooting on both sides,
⇒ a = ∛99 in
Since the cube root of 99 is 4.63, therefore, the length of the side of the cube is 4.63 in.
Example 2: What is the value of ∛99 + ∛(-99)?

Solution:

The cube root of -99 is equal to the negative of the cube root of 99.
i.e. ∛-99 = -∛99

Therefore, ∛99 + ∛(-99) = ∛99 - ∛99 = 0
Example 3: The volume of a spherical ball is 99π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 99π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 99
⇒ R = ∛(3/4 × 99) = ∛(3/4) × ∛99 = 0.90856 × 4.62607 (∵ ∛(3/4) = 0.90856 and ∛99 = 4.62607)
⇒ R = 4.20306 in³

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FAQs on Cube Root of 99

What is the Value of the Cube Root of 99?

We can express 99 as 3 × 3 × 11 i.e. ∛99 = ∛(3 × 3 × 11) = 4.62607. Therefore, the value of the cube root of 99 is 4.62607.

What is the Cube Root of -99?

The cube root of -99 is equal to the negative of the cube root of 99. Therefore, ∛-99 = -(∛99) = -(4.626) = -4.626.

What is the Cube of the Cube Root of 99?

The cube of the cube root of 99 is the number 99 itself i.e. (∛99)³ = (99^1/3)³ = 99.

Is 99 a Perfect Cube?

The number 99 on prime factorization gives 3 × 3 × 11. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 99 is irrational, hence 99 is not a perfect cube.

Why is the Value of the Cube Root of 99 Irrational?

The value of the cube root of 99 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛99 is irrational.

If the Cube Root of 99 is 4.63, Find the Value of ∛0.099.

Let us represent ∛0.099 in p/q form i.e. ∛(99/1000) = 4.63/10 = 0.46. Hence, the value of ∛0.099 = 0.46.