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Cube Root of 33

The value of the cube root of 33 rounded to 6 decimal places is 3.207534. It is the real solution of the equation x³ = 33. The cube root of 33 is expressed as ∛33 in the radical form and as (33)^⅓ or (33)^0.33 in the exponent form. The prime factorization of 33 is 3 × 11, hence, the cube root of 33 in its lowest radical form is expressed as ∛33.

Cube root of 33: 3.20753433
Cube root of 33 in Exponential Form: (33)^⅓
Cube root of 33 in Radical Form: ∛33

1.	What is the Cube Root of 33?
2.	How to Calculate the Cube Root of 33?
3.	Is the Cube Root of 33 Irrational?
4.	FAQs on Cube Root of 33

What is the Cube Root of 33?

The cube root of 33 is the number which when multiplied by itself three times gives the product as 33. Since 33 can be expressed as 3 × 11. Therefore, the cube root of 33 = ∛(3 × 11) = 3.2075.

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How to Calculate the Value of the Cube Root of 33?

Cube Root of 33 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 = 33
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 33]
⇒ x = 3
Therefore,
∛33 = 3 (3³ + 2 × 33)/(2 × 3³ + 33)) = 3.21
⇒ ∛33 ≈ 3.21
Therefore, the cube root of 33 is 3.21 approximately.

Is the Cube Root of 33 Irrational?

Yes, because ∛33 = ∛(3 × 11) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 33 is an irrational number.

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Cube Root of 33 Solved Examples

Example 1: Given the volume of a cube is 33 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 33 in³ = a³
⇒ a³ = 33
Cube rooting on both sides,
⇒ a = ∛33 in
Since the cube root of 33 is 3.21, therefore, the length of the side of the cube is 3.21 in.
Example 2: The volume of a spherical ball is 33π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 33π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 33
⇒ R = ∛(3/4 × 33) = ∛(3/4) × ∛33 = 0.90856 × 3.20753 (∵ ∛(3/4) = 0.90856 and ∛33 = 3.20753)
⇒ R = 2.91423 in³
Example 3: What is the value of ∛33 ÷ ∛(-33)?

Solution:

The cube root of -33 is equal to the negative of the cube root of 33.
⇒ ∛-33 = -∛33

Therefore,
⇒ ∛33/∛(-33) = ∛33/(-∛33) = -1

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FAQs on Cube Root of 33

What is the Value of the Cube Root of 33?

We can express 33 as 3 × 11 i.e. ∛33 = ∛(3 × 11) = 3.20753. Therefore, the value of the cube root of 33 is 3.20753.

What is the Cube Root of -33?

The cube root of -33 is equal to the negative of the cube root of 33. Therefore, ∛-33 = -(∛33) = -(3.208) = -3.208.

How to Simplify the Cube Root of 33/216?

We know that the cube root of 33 is 3.20753 and the cube root of 216 is 6. Therefore, ∛(33/216) = (∛33)/(∛216) = 3.208/6 = 0.5347.

If the Cube Root of 33 is 3.21, Find the Value of ∛0.033.

Let us represent ∛0.033 in p/q form i.e. ∛(33/1000) = 3.21/10 = 0.32. Hence, the value of ∛0.033 = 0.32.

Is 33 a Perfect Cube?

The number 33 on prime factorization gives 3 × 11. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 33 is irrational, hence 33 is not a perfect cube.

What is the Cube of the Cube Root of 33?

The cube of the cube root of 33 is the number 33 itself i.e. (∛33)³ = (33^1/3)³ = 33.