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Cube Root of 20

The value of the cube root of 20 rounded to 4 decimal places is 2.7144. It is the real solution of the equation x³ = 20. The cube root of 20 is expressed as ∛20 in the radical form and as (20)^⅓ or (20)^0.33 in the exponent form. The prime factorization of 20 is 2 × 2 × 5, hence, the cube root of 20 in its lowest radical form is expressed as ∛20.

Cube root of 20: 2.714417617
Cube root of 20 in Exponential Form: (20)^⅓
Cube root of 20 in Radical Form: ∛20

1.	What is the Cube Root of 20?
2.	How to Calculate the Cube Root of 20?
3.	Is the Cube Root of 20 Irrational?
4.	FAQs on Cube Root of 20

What is the Cube Root of 20?

The cube root of 20 is the number which when multiplied by itself three times gives the product as 20. Since 20 can be expressed as 2 × 2 × 5. Therefore, the cube root of 20 = ∛(2 × 2 × 5) = 2.7144.

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How to Calculate the Value of the Cube Root of 20?

Cube Root of 20 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 = 20
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 20]
⇒ x = 2
Therefore,
∛20 = 2 (2³ + 2 × 20)/(2 × 2³ + 20)) = 2.67
⇒ ∛20 ≈ 2.67
Therefore, the cube root of 20 is 2.67 approximately.

Is the Cube Root of 20 Irrational?

Yes, because ∛20 = ∛(2 × 2 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 20 is an irrational number.

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Cube Root of 20 Solved Examples

Example 1: The volume of a spherical ball is 20π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 20π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 20
⇒ R = ∛(3/4 × 20) = ∛(3/4) × ∛20 = 0.90856 × 2.71442 (∵ ∛(3/4) = 0.90856 and ∛20 = 2.71442)
⇒ R = 2.46621 in³
Example 2: What is the value of ∛20 ÷ ∛(-20)?

Solution:

The cube root of -20 is equal to the negative of the cube root of 20.
⇒ ∛-20 = -∛20

Therefore,
⇒ ∛20/∛(-20) = ∛20/(-∛20) = -1
Example 3: Given the volume of a cube is 20 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 20 in³ = a³
⇒ a³ = 20
Cube rooting on both sides,
⇒ a = ∛20 in
Since the cube root of 20 is 2.71, therefore, the length of the side of the cube is 2.71 in.

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FAQs on Cube Root of 20

What is the Value of the Cube Root of 20?

We can express 20 as 2 × 2 × 5 i.e. ∛20 = ∛(2 × 2 × 5) = 2.71442. Therefore, the value of the cube root of 20 is 2.71442.

What is the Cube Root of -20?

The cube root of -20 is equal to the negative of the cube root of 20. Therefore, ∛-20 = -(∛20) = -(2.714) = -2.714.

What is the Value of 15 Plus 18 Cube Root 20?

The value of ∛20 is 2.714. So, 15 + 18 × ∛20 = 15 + 18 × 2.714 = 63.852. Hence, the value of 15 plus 18 cube root 20 is 63.852.

Is 20 a Perfect Cube?

The number 20 on prime factorization gives 2 × 2 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 20 is irrational, hence 20 is not a perfect cube.

Why is the Value of the Cube Root of 20 Irrational?

The value of the cube root of 20 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛20 is irrational.

What is the Cube of the Cube Root of 20?

The cube of the cube root of 20 is the number 20 itself i.e. (∛20)³ = (20^1/3)³ = 20.