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Cube Root of 243

The value of the cube root of 243 rounded to 6 decimal places is 6.240251. It is the real solution of the equation x³ = 243. The cube root of 243 is expressed as ∛243 or 3 ∛9 in the radical form and as (243)^⅓ or (243)^0.33 in the exponent form. The prime factorization of 243 is 3 × 3 × 3 × 3 × 3, hence, the cube root of 243 in its lowest radical form is expressed as 3 ∛9.

Cube root of 243: 6.240251469
Cube root of 243 in Exponential Form: (243)^⅓
Cube root of 243 in Radical Form: ∛243 or 3 ∛9

Cube Root of 243

1.	What is the Cube Root of 243?
2.	How to Calculate the Cube Root of 243?
3.	Is the Cube Root of 243 Irrational?
4.	FAQs on Cube Root of 243

What is the Cube Root of 243?

The cube root of 243 is the number which when multiplied by itself three times gives the product as 243. Since 243 can be expressed as 3 × 3 × 3 × 3 × 3. Therefore, the cube root of 243 = ∛(3 × 3 × 3 × 3 × 3) = 6.2403.

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How to Calculate the Value of the Cube Root of 243?

Cube Root of 243 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 = 243
Let us assume x as 6
[∵ 6³ = 216 and 216 is the nearest perfect cube that is less than 243]
⇒ x = 6
Therefore,
∛243 = 6 (6³ + 2 × 243)/(2 × 6³ + 243)) = 6.24
⇒ ∛243 ≈ 6.24
Therefore, the cube root of 243 is 6.24 approximately.

Is the Cube Root of 243 Irrational?

Yes, because ∛243 = ∛(3 × 3 × 3 × 3 × 3) = 3 ∛9 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 243 is an irrational number.

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Cube Root of 243 Solved Examples

Example 1: Given the volume of a cube is 243 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 243 in³ = a³
⇒ a³ = 243
Cube rooting on both sides,
⇒ a = ∛243 in
Since the cube root of 243 is 6.24, therefore, the length of the side of the cube is 6.24 in.
Example 2: Find the real root of the equation x³ − 243 = 0.

Solution:

x³ − 243 = 0 i.e. x³ = 243
Solving for x gives us,
x = ∛243, x = ∛243 × (-1 + √3i))/2 and x = ∛243 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛243
Therefore, the real root of the equation x³ − 243 = 0 is for x = ∛243 = 6.2403.
Example 3: What is the value of ∛243 ÷ ∛(-243)?

Solution:

The cube root of -243 is equal to the negative of the cube root of 243.
⇒ ∛-243 = -∛243

Therefore,
⇒ ∛243/∛(-243) = ∛243/(-∛243) = -1

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FAQs on Cube Root of 243

What is the Value of the Cube Root of 243?

We can express 243 as 3 × 3 × 3 × 3 × 3 i.e. ∛243 = ∛(3 × 3 × 3 × 3 × 3) = 6.24025. Therefore, the value of the cube root of 243 is 6.24025.

What is the Cube of the Cube Root of 243?

The cube of the cube root of 243 is the number 243 itself i.e. (∛243)³ = (243^1/3)³ = 243.

Why is the Value of the Cube Root of 243 Irrational?

The value of the cube root of 243 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛243 is irrational.

What is the Value of 12 Plus 18 Cube Root 243?

The value of ∛243 is 6.24. So, 12 + 18 × ∛243 = 12 + 18 × 6.24 = 124.32000000000001. Hence, the value of 12 plus 18 cube root 243 is 124.32000000000001.

If the Cube Root of 243 is 6.24, Find the Value of ∛0.243.

Let us represent ∛0.243 in p/q form i.e. ∛(243/1000) = 6.24/10 = 0.62. Hence, the value of ∛0.243 = 0.62.

What is the Cube Root of -243?

The cube root of -243 is equal to the negative of the cube root of 243. Therefore, ∛-243 = -(∛243) = -(6.24) = -6.24.

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