Cube Root of 250

The cube root of 250 is a natural number that has a cube of 250. 250 has a cube root of around 6.299. Getting an integer’s cube root is the opposite of cubing an integer. The square root and cube root are denoted by the radicals “√” and “∛”, respectively. The cube root of 250 is represented exponentially by the number 250^1/3. Let’s look at several approaches to finding the cube root of 250.

Also, read:How to Find Cube Root?

What is the Cube Root of 250?

The cube root of 250 is the number whose cube is 250. The cube of an integer is a perfect cube. Because it is not the cube of any integer, 250 is not a perfect cube number. 250 is also a composite number. A thorough explanation of how to compute the cube root of 250 is given in this article.

Also, try out:Cube Root Calculator.

How to Find the Cube Root of 250?

Let’s now determine the cube root of 250. In this article, we’ll look at it from various perspectives.

Finding Cube Root of 250 by Prime Factorisation Method

The list of procedures below describes how to get an integer’s cube root using the prime factorisation technique.

• Get the prime factors of the number.
• Make a group of three for each prime factor in the prime factorisation.
• For each group, a single occurrence of the factor is selected, followed by the multiplication of all the prime factors. A factor could not be further simplified if it cannot be broken into three.

Let’s apply the prime factorisation method to get the cube root of 250.

As is well known, the prime factorisation of 250 is 2 × 5 × 5 × 5.

Therefore, the cube root of 250 is:

∛250 = ∛(2 × 5 × 5 × 5) = 5∛2.

Since 5∛2 cannot be simplified further, its cube root is also an irrational number.

Finding Cube Root of 250 by Approximation Method

Halley’s approach, often known as an approximation method, can be used to get the cube root of any integer. Using Halley’s method, the cube root of 250 may be determined as illustrated below:

Halley’s Cube Root Formula:

Where

The necessary cube root calculation is represented by the letter “a”.

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

In this case, a = 250

Using x = 6, we will have 6³ = 216 < 250

Using Halley’s formula, the cube root of 250 is calculated, and the results are highly comparable.

∛250 = 6[(6³ + 2 × 250)/(2 × 6³ + 250)]

∛250 = 6[(216 + 500)/(432 + 250)]

∛250 = 6[716/682]

∛250 = 6[1.049] ≈ 6.294, which is quite near to cube root of 250.

The cube root of 250 is calculated to be 6.294 using Halley’s formula.

Video Lesson on Finding Cube Roots

Related Articles

• Cube Root Table
• Cube Root 1 to 20
• Cube Root of Unity
• Cube Root of 1 to 30
• Cube Root of 2
• Cube Root of 64
• Cube Root of 3
• Cube Root of 4

Solved Examples on Cube Root of 250

Example 1:

Find the value of x, if ∛250x = 10(6.299).

Solution:

Given equation: ∛250x = 10 (6.299).

As we already know, the cube root of 250 is about equal to 6.299.

In the equation above, if ∛250 = 6.299 is replaced, we get,

6.299 x = 10 (6.299)

⇒ x = [10(6.299)] /6.299

⇒ x = 10.

As a result, x = 10.

Example 2:

Find the lowest integer that, when multiplied by 250, produces a perfect cube number.

Solution:

250 has a prime factorisation of 2 × 5 × 5 × 5, which is a well-known value.

Each factor has to be grouped by three to get the cube root of 250. Therefore, we need to multiply 250 by 2 × 2.

As a result, we have

250 × 2 × 2 = 250 × 4 = 1000

Hence, 1000 is a perfect cube number.

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

Therefore, 4 is the least number that can be multiplied by 250 to get the perfect cube number.

Example 3:

Calculate the lengths of the sides of a cube having a volume of 250 cm³.

Solution:

Assume that “a” represents the cube’s side length.

This means that the cube’s volume is a³ = 250 cm³.

We get to a = ∛250 = 6.299 (approximately) by calculating the cube roots on both sides of the equation.

Therefore, “a” is about equivalent to 6.299.