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Cube Root of 250

The value of the cube root of 250 rounded to 7 decimal places is 6.2996052. It is the real solution of the equation x³ = 250. The cube root of 250 is expressed as ∛250 or 5 ∛2 in the radical form and as (250)^⅓ or (250)^0.33 in the exponent form. The prime factorization of 250 is 2 × 5 × 5 × 5, hence, the cube root of 250 in its lowest radical form is expressed as 5 ∛2.

Cube root of 250: 6.299605249
Cube root of 250 in Exponential Form: (250)^⅓
Cube root of 250 in Radical Form: ∛250 or 5 ∛2

Cube Root of 250

1.	What is the Cube Root of 250?
2.	How to Calculate the Cube Root of 250?
3.	Is the Cube Root of 250 Irrational?
4.	FAQs on Cube Root of 250

What is the Cube Root of 250?

The cube root of 250 is the number which when multiplied by itself three times gives the product as 250. Since 250 can be expressed as 2 × 5 × 5 × 5. Therefore, the cube root of 250 = ∛(2 × 5 × 5 × 5) = 6.2996.

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How to Calculate the Value of the Cube Root of 250?

Cube Root of 250 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 = 250
Let us assume x as 6
[∵ 6³ = 216 and 216 is the nearest perfect cube that is less than 250]
⇒ x = 6
Therefore,
∛250 = 6 (6³ + 2 × 250)/(2 × 6³ + 250)) = 6.3
⇒ ∛250 ≈ 6.3
Therefore, the cube root of 250 is 6.3 approximately.

Is the Cube Root of 250 Irrational?

Yes, because ∛250 = ∛(2 × 5 × 5 × 5) = 5 ∛2 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 250 is an irrational number.

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Cube Root of 250 Solved Examples

Example 1: Find the real root of the equation x³ − 250 = 0.

Solution:

x³ − 250 = 0 i.e. x³ = 250
Solving for x gives us,
x = ∛250, x = ∛250 × (-1 + √3i))/2 and x = ∛250 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛250
Therefore, the real root of the equation x³ − 250 = 0 is for x = ∛250 = 6.2996.
Example 2: The volume of a spherical ball is 250π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 250π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 250
⇒ R = ∛(3/4 × 250) = ∛(3/4) × ∛250 = 0.90856 × 6.29961 (∵ ∛(3/4) = 0.90856 and ∛250 = 6.29961)
⇒ R = 5.72357 in³
Example 3: What is the value of ∛250 ÷ ∛(-250)?

Solution:

The cube root of -250 is equal to the negative of the cube root of 250.
⇒ ∛-250 = -∛250

Therefore,
⇒ ∛250/∛(-250) = ∛250/(-∛250) = -1

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FAQs on Cube Root of 250

What is the Value of the Cube Root of 250?

We can express 250 as 2 × 5 × 5 × 5 i.e. ∛250 = ∛(2 × 5 × 5 × 5) = 6.29961. Therefore, the value of the cube root of 250 is 6.29961.

If the Cube Root of 250 is 6.3, Find the Value of ∛0.25.

Let us represent ∛0.25 in p/q form i.e. ∛(250/1000) = 6.3/10 = 0.63. Hence, the value of ∛0.25 = 0.63.

Is 250 a Perfect Cube?

The number 250 on prime factorization gives 2 × 5 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 250 is irrational, hence 250 is not a perfect cube.

What is the Value of 18 Plus 2 Cube Root 250?

The value of ∛250 is 6.3. So, 18 + 2 × ∛250 = 18 + 2 × 6.3 = 30.6. Hence, the value of 18 plus 2 cube root 250 is 30.6.

What is the Cube of the Cube Root of 250?

The cube of the cube root of 250 is the number 250 itself i.e. (∛250)³ = (250^1/3)³ = 250.

Why is the Value of the Cube Root of 250 Irrational?

The value of the cube root of 250 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛250 is irrational.

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