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Cube Root of 50

The value of the cube root of 50 rounded to 4 decimal places is 3.684. It is the real solution of the equation x³ = 50. The cube root of 50 is expressed as ∛50 in the radical form and as (50)^⅓ or (50)^0.33 in the exponent form. The prime factorization of 50 is 2 × 5 × 5, hence, the cube root of 50 in its lowest radical form is expressed as ∛50.

Cube root of 50: 3.684031499
Cube root of 50 in Exponential Form: (50)^⅓
Cube root of 50 in Radical Form: ∛50

Cube Root of 50

1.	What is the Cube Root of 50?
2.	How to Calculate the Cube Root of 50?
3.	Is the Cube Root of 50 Irrational?
4.	FAQs on Cube Root of 50

What is the Cube Root of 50?

The cube root of 50 is the number which when multiplied by itself three times gives the product as 50. Since 50 can be expressed as 2 × 5 × 5. Therefore, the cube root of 50 = ∛(2 × 5 × 5) = 3.684.

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How to Calculate the Value of the Cube Root of 50?

Cube Root of 50 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 = 50
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 50]
⇒ x = 3
Therefore,
∛50 = 3 (3³ + 2 × 50)/(2 × 3³ + 50)) = 3.66
⇒ ∛50 ≈ 3.66
Therefore, the cube root of 50 is 3.66 approximately.

Is the Cube Root of 50 Irrational?

Yes, because ∛50 = ∛(2 × 5 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 50 is an irrational number.

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Cube Root of 50 Solved Examples

Example 1: Given the volume of a cube is 50 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 50 in³ = a³
⇒ a³ = 50
Cube rooting on both sides,
⇒ a = ∛50 in
Since the cube root of 50 is 3.68, therefore, the length of the side of the cube is 3.68 in.
Example 2: Find the real root of the equation x³ − 50 = 0.

Solution:

x³ − 50 = 0 i.e. x³ = 50
Solving for x gives us,
x = ∛50, x = ∛50 × (-1 + √3i))/2 and x = ∛50 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛50
Therefore, the real root of the equation x³ − 50 = 0 is for x = ∛50 = 3.684.
Example 3: What is the value of ∛50 ÷ ∛(-50)?

Solution:

The cube root of -50 is equal to the negative of the cube root of 50.
⇒ ∛-50 = -∛50

Therefore,
⇒ ∛50/∛(-50) = ∛50/(-∛50) = -1

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FAQs on Cube Root of 50

What is the Value of the Cube Root of 50?

We can express 50 as 2 × 5 × 5 i.e. ∛50 = ∛(2 × 5 × 5) = 3.68403. Therefore, the value of the cube root of 50 is 3.68403.

How to Simplify the Cube Root of 50/27?

We know that the cube root of 50 is 3.68403 and the cube root of 27 is 3. Therefore, ∛(50/27) = (∛50)/(∛27) = 3.684/3 = 1.228.

If the Cube Root of 50 is 3.68, Find the Value of ∛0.05.

Let us represent ∛0.05 in p/q form i.e. ∛(50/1000) = 3.68/10 = 0.37. Hence, the value of ∛0.05 = 0.37.

What is the Value of 8 Plus 19 Cube Root 50?

The value of ∛50 is 3.684. So, 8 + 19 × ∛50 = 8 + 19 × 3.684 = 77.99600000000001. Hence, the value of 8 plus 19 cube root 50 is 77.99600000000001.

Why is the Value of the Cube Root of 50 Irrational?

The value of the cube root of 50 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛50 is irrational.

Is 50 a Perfect Cube?

The number 50 on prime factorization gives 2 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 50 is irrational, hence 50 is not a perfect cube.

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