Cube Root of 50

The cube root of 50 is a natural number whose cube is 50. 50 has a cube root of around 3.684. Calculating an integer’s cube root is the inverse of cubing an integer. The square root and cube root are represented by the radical symbols “√” and “∛”, respectively. The cube root of 50 is represented exponentially by 50^1/3. Let’s look at several approaches to finding the cube root of 50.

Also, read:How to Find Cube Root?

What is the Cube Root of 50?

The cube root of 50 is the number whose cube is 50. The cube of an integer is perfect cube. Since 50 is not the cube of any integer, it is not a perfect cube number. 50 is a composite number as well. This article extensively describes how to compute the cube root of 50.

Also, try out:Cube Root Calculator.

How to Find the Cube Root of 50?

Let’s now determine the 50’s cube root. In this article, we will explore it from a variety of perspectives.

Finding Cube Root of 50 by Prime Factorisation Method

The cube root of an integer may be calculated using the prime factorisation method, as shown in the list of steps below.

• Get the prime factors of the number.
• Make a group of three for each prime factor in the prime factorisation.
• Only one occurrence of the factor is picked for each group, and then all of the prime factors are multiplied. A factor cannot be further simplified if it cannot be broken into three.

Let’s determine the cube root of 50 using the prime factorisation method.

As is well known, 2 × 5 × 5 is the prime factorisation of 50.

Hence, the cube root of 50 is:

= ∛(2 × 5 × 5) = ∛50

Since ∛50 cannot be decreased further, 50’s cube root is also an irrational number.

Finding Cube Root of 50 by Approximation Method

We may calculate the cube root of any integer using Halley’s approach, sometimes referred to as an approximation method. Using Halley’s method, the cube root of 50 can be determined as illustrated below:

Halley’s Cube Root Formula:

Where

The required cube root calculation is symbolized by the letter “a”.

To get the estimated value, take the cube root of the closest perfect cube, “x”.

In this case, a = 50

By substituting x = 3, we will get 3³ = 27 < 50

Using Halley’s formula, the cube root of 50 is calculated, and the result is fairly comparable.

∛50 = 3[(3³ + 2 × 50)/(2 × 3³ + 50)]

∛50 = 3[(27 + 100)/(54 + 50)]

∛50 = 3[127/104]

∛50 = 3[1.22] ≈ 3.66, which is really quite close to the cube root of 50.

The cube root of 50 is calculated using Halley’s formula to be 3.66.

Video Lesson on Finding Cube Roots

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• Cube Root Table
• Cube Root of 216
• Cube Root of 729
• Cube Root 1 to 20
• Cube Root 1 to 30

Solved Examples on Cube Root of 50

Example 1:

Calculate the value of x, if ∛50x = 5 (3.684).

Solution:

The provided equation is ∛50x = 5 (3.684).

As we know, the cube root of 50 is about equivalent to 3.684.

In the preceding equation, if ∛50 = 3.684 is replaced, we get

3.684 x = 5 (3.684)

⇒ x = [5(3.684)] /3.684

⇒ x = 5.

Thus, x is equal to 5.

Example 2:

Determine the smallest integer that can be multiplied by 50 to get a perfect cube number

Solution:

The prime factorisation of 50 is 2 × 5 × 5, as is well known.

Each element must be grouped by three to calculate the cube root of 50. Therefore, we need to multiply 50 by 2 × 2 × 5.

Therefore, we obtain,

50 × 2 × 2 × 5 = 50 × 20 = 1000

Therefore, 1000 is a perfect cube number.

Thus, the cube root of 1000 is ∛(2 × 2 × 2 × 5 × 5 × 5 ) = 2 × 5 = 10

Therefore, 20 is the lowest number that may be multiplied by 50 to get the perfect cube number.

Example 3:

Determine the side lengths of a cube having a volume of 50 cm³.

Solution:

Use “a” as the cube’s side length.

Therefore, the cube’s volume is equal to a³ = 50 cm³.

We obtain a = ∛50 = 3.684 cm (approx), by taking the cube roots on two sides of the equation.

Thus, “a” has a value of around 3.684.