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Cube Root of 486

The value of the cube root of 486 rounded to 4 decimal places is 7.8622. It is the real solution of the equation x³ = 486. The cube root of 486 is expressed as ∛486 or 3 ∛18 in the radical form and as (486)^⅓ or (486)^0.33 in the exponent form. The prime factorization of 486 is 2 × 3 × 3 × 3 × 3 × 3, hence, the cube root of 486 in its lowest radical form is expressed as 3 ∛18.

Cube root of 486: 7.862224183
Cube root of 486 in Exponential Form: (486)^⅓
Cube root of 486 in Radical Form: ∛486 or 3 ∛18

Cube Root of 486

1.	What is the Cube Root of 486?
2.	How to Calculate the Cube Root of 486?
3.	Is the Cube Root of 486 Irrational?
4.	FAQs on Cube Root of 486

What is the Cube Root of 486?

The cube root of 486 is the number which when multiplied by itself three times gives the product as 486. Since 486 can be expressed as 2 × 3 × 3 × 3 × 3 × 3. Therefore, the cube root of 486 = ∛(2 × 3 × 3 × 3 × 3 × 3) = 7.8622.

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How to Calculate the Value of the Cube Root of 486?

Cube Root of 486 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 = 486
Let us assume x as 7
[∵ 7³ = 343 and 343 is the nearest perfect cube that is less than 486]
⇒ x = 7
Therefore,
∛486 = 7 (7³ + 2 × 486)/(2 × 7³ + 486)) = 7.85
⇒ ∛486 ≈ 7.85
Therefore, the cube root of 486 is 7.85 approximately.

Is the Cube Root of 486 Irrational?

Yes, because ∛486 = ∛(2 × 3 × 3 × 3 × 3 × 3) = 3 ∛18 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 486 is an irrational number.

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Cube Root of 486 Solved Examples

Example 1: Find the real root of the equation x³ − 486 = 0.

Solution:

x³ − 486 = 0 i.e. x³ = 486
Solving for x gives us,
x = ∛486, x = ∛486 × (-1 + √3i))/2 and x = ∛486 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛486
Therefore, the real root of the equation x³ − 486 = 0 is for x = ∛486 = 7.8622.
Example 2: The volume of a spherical ball is 486π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 486π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 486
⇒ R = ∛(3/4 × 486) = ∛(3/4) × ∛486 = 0.90856 × 7.86222 (∵ ∛(3/4) = 0.90856 and ∛486 = 7.86222)
⇒ R = 7.1433 in³
Example 3: Given the volume of a cube is 486 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 486 in³ = a³
⇒ a³ = 486
Cube rooting on both sides,
⇒ a = ∛486 in
Since the cube root of 486 is 7.86, therefore, the length of the side of the cube is 7.86 in.

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FAQs on Cube Root of 486

What is the Value of the Cube Root of 486?

We can express 486 as 2 × 3 × 3 × 3 × 3 × 3 i.e. ∛486 = ∛(2 × 3 × 3 × 3 × 3 × 3) = 7.86222. Therefore, the value of the cube root of 486 is 7.86222.

If the Cube Root of 486 is 7.86, Find the Value of ∛0.486.

Let us represent ∛0.486 in p/q form i.e. ∛(486/1000) = 7.86/10 = 0.79. Hence, the value of ∛0.486 = 0.79.

What is the Cube of the Cube Root of 486?

The cube of the cube root of 486 is the number 486 itself i.e. (∛486)³ = (486^1/3)³ = 486.

Why is the Value of the Cube Root of 486 Irrational?

The value of the cube root of 486 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛486 is irrational.

What is the Value of 15 Plus 19 Cube Root 486?

The value of ∛486 is 7.862. So, 15 + 19 × ∛486 = 15 + 19 × 7.862 = 164.37800000000001. Hence, the value of 15 plus 19 cube root 486 is 164.37800000000001.

How to Simplify the Cube Root of 486/125?

We know that the cube root of 486 is 7.86222 and the cube root of 125 is 5. Therefore, ∛(486/125) = (∛486)/(∛125) = 7.862/5 = 1.5724.

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