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Cube Root of 21

The value of the cube root of 21 rounded to 7 decimal places is 2.7589242. It is the real solution of the equation x³ = 21. The cube root of 21 is expressed as ∛21 in the radical form and as (21)^⅓ or (21)^0.33 in the exponent form. The prime factorization of 21 is 3 × 7, hence, the cube root of 21 in its lowest radical form is expressed as ∛21.

Cube root of 21: 2.758924176
Cube root of 21 in Exponential Form: (21)^⅓
Cube root of 21 in Radical Form: ∛21

1.	What is the Cube Root of 21?
2.	How to Calculate the Cube Root of 21?
3.	Is the Cube Root of 21 Irrational?
4.	FAQs on Cube Root of 21

What is the Cube Root of 21?

The cube root of 21 is the number which when multiplied by itself three times gives the product as 21. Since 21 can be expressed as 3 × 7. Therefore, the cube root of 21 = ∛(3 × 7) = 2.7589.

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How to Calculate the Value of the Cube Root of 21?

Cube Root of 21 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 = 21
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 21]
⇒ x = 2
Therefore,
∛21 = 2 (2³ + 2 × 21)/(2 × 2³ + 21)) = 2.7
⇒ ∛21 ≈ 2.7
Therefore, the cube root of 21 is 2.7 approximately.

Is the Cube Root of 21 Irrational?

Yes, because ∛21 = ∛(3 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 21 is an irrational number.

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Cube Root of 21 Solved Examples

Example 1: Find the real root of the equation x³ − 21 = 0.

Solution:

x³ − 21 = 0 i.e. x³ = 21
Solving for x gives us,
x = ∛21, x = ∛21 × (-1 + √3i))/2 and x = ∛21 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛21
Therefore, the real root of the equation x³ − 21 = 0 is for x = ∛21 = 2.7589.
Example 2: Given the volume of a cube is 21 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 21 in³ = a³
⇒ a³ = 21
Cube rooting on both sides,
⇒ a = ∛21 in
Since the cube root of 21 is 2.76, therefore, the length of the side of the cube is 2.76 in.
Example 3: What is the value of ∛21 + ∛(-21)?

Solution:

The cube root of -21 is equal to the negative of the cube root of 21.
i.e. ∛-21 = -∛21

Therefore, ∛21 + ∛(-21) = ∛21 - ∛21 = 0

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FAQs on Cube Root of 21

What is the Value of the Cube Root of 21?

We can express 21 as 3 × 7 i.e. ∛21 = ∛(3 × 7) = 2.75892. Therefore, the value of the cube root of 21 is 2.75892.

If the Cube Root of 21 is 2.76, Find the Value of ∛0.021.

Let us represent ∛0.021 in p/q form i.e. ∛(21/1000) = 2.76/10 = 0.28. Hence, the value of ∛0.021 = 0.28.

What is the Cube Root of -21?

The cube root of -21 is equal to the negative of the cube root of 21. Therefore, ∛-21 = -(∛21) = -(2.759) = -2.759.

How to Simplify the Cube Root of 21/512?

We know that the cube root of 21 is 2.75892 and the cube root of 512 is 8. Therefore, ∛(21/512) = (∛21)/(∛512) = 2.759/8 = 0.3449.

What is the Value of 15 Plus 1 Cube Root 21?

The value of ∛21 is 2.759. So, 15 + 1 × ∛21 = 15 + 1 × 2.759 = 17.759. Hence, the value of 15 plus 1 cube root 21 is 17.759.

What is the Cube of the Cube Root of 21?

The cube of the cube root of 21 is the number 21 itself i.e. (∛21)³ = (21^1/3)³ = 21.