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Cube Root of 81

The value of the cube root of 81 rounded to 6 decimal places is 4.326749. It is the real solution of the equation x³ = 81. The cube root of 81 is expressed as ∛81 or 3 ∛3 in the radical form and as (81)^⅓ or (81)^0.33 in the exponent form. The prime factorization of 81 is 3 × 3 × 3 × 3, hence, the cube root of 81 in its lowest radical form is expressed as 3 ∛3.

Cube root of 81: 4.326748711
Cube root of 81 in Exponential Form: (81)^⅓
Cube root of 81 in Radical Form: ∛81 or 3 ∛3

1.	What is the Cube Root of 81?
2.	How to Calculate the Cube Root of 81?
3.	Is the Cube Root of 81 Irrational?
4.	FAQs on Cube Root of 81

What is the Cube Root of 81?

The cube root of 81 is the number which when multiplied by itself three times gives the product as 81. Since 81 can be expressed as 3 × 3 × 3 × 3. Therefore, the cube root of 81 = ∛(3 × 3 × 3 × 3) = 4.3267.

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How to Calculate the Value of the Cube Root of 81?

Cube Root of 81 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 = 81
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 81]
⇒ x = 4
Therefore,
∛81 = 4 (4³ + 2 × 81)/(2 × 4³ + 81)) = 4.33
⇒ ∛81 ≈ 4.33
Therefore, the cube root of 81 is 4.33 approximately.

Is the Cube Root of 81 Irrational?

Yes, because ∛81 = ∛(3 × 3 × 3 × 3) = 3 ∛3 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 81 is an irrational number.

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Cube Root of 81 Solved Examples

Example 1: The volume of a spherical ball is 81π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 81π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 81
⇒ R = ∛(3/4 × 81) = ∛(3/4) × ∛81 = 0.90856 × 4.32675 (∵ ∛(3/4) = 0.90856 and ∛81 = 4.32675)
⇒ R = 3.93111 in³
Example 2: Given the volume of a cube is 81 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 81 in³ = a³
⇒ a³ = 81
Cube rooting on both sides,
⇒ a = ∛81 in
Since the cube root of 81 is 4.33, therefore, the length of the side of the cube is 4.33 in.
Example 3: What is the value of ∛81 + ∛(-81)?

Solution:

The cube root of -81 is equal to the negative of the cube root of 81.
i.e. ∛-81 = -∛81

Therefore, ∛81 + ∛(-81) = ∛81 - ∛81 = 0

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FAQs on Cube Root of 81

What is the Value of the Cube Root of 81?

We can express 81 as 3 × 3 × 3 × 3 i.e. ∛81 = ∛(3 × 3 × 3 × 3) = 4.32675. Therefore, the value of the cube root of 81 is 4.32675.

What is the Cube Root of -81?

The cube root of -81 is equal to the negative of the cube root of 81. Therefore, ∛-81 = -(∛81) = -(4.327) = -4.327.

What is the Value of 5 Plus 8 Cube Root 81?

The value of ∛81 is 4.327. So, 5 + 8 × ∛81 = 5 + 8 × 4.327 = 39.616. Hence, the value of 5 plus 8 cube root 81 is 39.616.

Is 81 a Perfect Cube?

The number 81 on prime factorization gives 3 × 3 × 3 × 3. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 81 is irrational, hence 81 is not a perfect cube.

Why is the Value of the Cube Root of 81 Irrational?

The value of the cube root of 81 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛81 is irrational.

What is the Cube of the Cube Root of 81?

The cube of the cube root of 81 is the number 81 itself i.e. (∛81)³ = (81^1/3)³ = 81.