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Cube Root of 22

The value of the cube root of 22 rounded to 4 decimal places is 2.802. It is the real solution of the equation x³ = 22. The cube root of 22 is expressed as ∛22 in the radical form and as (22)^⅓ or (22)^0.33 in the exponent form. The prime factorization of 22 is 2 × 11, hence, the cube root of 22 in its lowest radical form is expressed as ∛22.

Cube root of 22: 2.802039331
Cube root of 22 in Exponential Form: (22)^⅓
Cube root of 22 in Radical Form: ∛22

1.	What is the Cube Root of 22?
2.	How to Calculate the Cube Root of 22?
3.	Is the Cube Root of 22 Irrational?
4.	FAQs on Cube Root of 22

What is the Cube Root of 22?

The cube root of 22 is the number which when multiplied by itself three times gives the product as 22. Since 22 can be expressed as 2 × 11. Therefore, the cube root of 22 = ∛(2 × 11) = 2.802.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 22?

Cube Root of 22 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 = 22
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 22]
⇒ x = 2
Therefore,
∛22 = 2 (2³ + 2 × 22)/(2 × 2³ + 22)) = 2.74
⇒ ∛22 ≈ 2.74
Therefore, the cube root of 22 is 2.74 approximately.

Is the Cube Root of 22 Irrational?

Yes, because ∛22 = ∛(2 × 11) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 22 is an irrational number.

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Cube Root of 22 Solved Examples

Example 1: What is the value of ∛22 ÷ ∛(-22)?

Solution:

The cube root of -22 is equal to the negative of the cube root of 22.
⇒ ∛-22 = -∛22

Therefore,
⇒ ∛22/∛(-22) = ∛22/(-∛22) = -1
Example 2: The volume of a spherical ball is 22π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 22π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 22
⇒ R = ∛(3/4 × 22) = ∛(3/4) × ∛22 = 0.90856 × 2.80204 (∵ ∛(3/4) = 0.90856 and ∛22 = 2.80204)
⇒ R = 2.54582 in³
Example 3: Given the volume of a cube is 22 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 22 in³ = a³
⇒ a³ = 22
Cube rooting on both sides,
⇒ a = ∛22 in
Since the cube root of 22 is 2.8, therefore, the length of the side of the cube is 2.8 in.

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FAQs on Cube Root of 22

What is the Value of the Cube Root of 22?

We can express 22 as 2 × 11 i.e. ∛22 = ∛(2 × 11) = 2.80204. Therefore, the value of the cube root of 22 is 2.80204.

If the Cube Root of 22 is 2.8, Find the Value of ∛0.022.

Let us represent ∛0.022 in p/q form i.e. ∛(22/1000) = 2.8/10 = 0.28. Hence, the value of ∛0.022 = 0.28.

What is the Value of 18 Plus 20 Cube Root 22?

The value of ∛22 is 2.802. So, 18 + 20 × ∛22 = 18 + 20 × 2.802 = 74.03999999999999. Hence, the value of 18 plus 20 cube root 22 is 74.03999999999999.

Is 22 a Perfect Cube?

The number 22 on prime factorization gives 2 × 11. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 22 is irrational, hence 22 is not a perfect cube.

What is the Cube Root of -22?

The cube root of -22 is equal to the negative of the cube root of 22. Therefore, ∛-22 = -(∛22) = -(2.802) = -2.802.

How to Simplify the Cube Root of 22/216?

We know that the cube root of 22 is 2.80204 and the cube root of 216 is 6. Therefore, ∛(22/216) = (∛22)/(∛216) = 2.802/6 = 0.467.