IS 250 is a perfect cube?

Here we will show you how to get the factors of cube root of 250 (factors of ∛250). We define factors of cube root of 250 as any integer (whole number) or cube root that you can evenly divide into cube root of 250. Furthermore, if you divide ∛250 by a factor of ∛250, it will result in another factor of ∛250.

First, we will find all the cube roots that we can evenly divide into cube root of 250. We do this by finding all the factors of 250 and add a radical (∛) to them like this:

∛1, ∛2, ∛5, ∛10, ∛25, ∛50, ∛125, and ∛250

Next, we will find all the integers that we can evenly divide into cube root of 250. We do that by first identifying the perfect cube roots from the list above:

∛1 and ∛125

Then, we take the cube root of the perfect cube roots to get the integers that we can evenly divide into cube root of 250.

1 and 5

Factors of cube root of 250 are the two lists above combined. Thus, factors of cube root of 250 (cube roots and integers) are as follows:

1, 5, ∛1, ∛2, ∛5, ∛10, ∛25, ∛50, ∛125, and ∛250

Like we said above, cube root of 250 divided by any of its factors, will result in another of its factors. Therefore, if you divide ∛250 by any of factors above, you will see that it results in one of the other factors.

What can you do with this information? For one, you can get cube root of 250 in its simplest form. Cube root of 250 simplified is the largest integer factor times the cube root of 250 divided by the largest perfect cube root. Thus, here is the math to get cube root of 250 in its simplest radical form:

If the prime factors of a number are grouped in triples of equal factors, then that number is called a perfect cube.

Examples to find if the given number is a perfect cube:

1. Find out if the following are perfect cubes.

(i) 250

(ii) 5832

(i) 250

Solution: 

Resolving 250 as the product of prime factors

250 = 2 × 5 × 5 × 5

Since 2 does not exist in product of triples.

Therefore, 250 is not a perfect cube. 

(ii) 5832

Solution:

Resolving 5832 as the product of prime factors

5832 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

Since, they are grouped in triples.

Therefore, 5832 is a perfect cube.

2. Find the smallest number by which 1944 must be multiplied so that the product is a perfect cube.

Solution:

Resolving 1944 as the product of prime factors

1944 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3

In order to make 1944 a perfect cube, it must be multiplied by 3.

3. Find the smallest number by which 4394 must be divided so that the quotient is a perfect cube.

Solution:

Resolving 4394 as the product of primes

4394 = 2 × 13 × 13 × 13

In order to make 4394 a perfect cube, it must be divided by 2, so that the quotient is 2197.

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In math, the cube root of a number like 250 is a number that, when multiplied by itself two times, is equal to 250.

We would show this in mathematical form with the cube root symbol, which is similar to the radical symbol (√) used in a square root, but which also has the number 3 above the symbol (this number is called the index):

∛250

So, the √ is called the radical symbol, the little 3 above it is the index (which means multiply by itself two more times), and the number, 250, is called the radicand.

To explain the cube root a little more, the cube root of the number 250 is a number (which we call n) that when multiplied by itself twice is equal to 250:

n × n × n = 250

∛250 is the same as 250⅓ and so if you are solving a problem in a spreadsheet like Excel, Numbers, or Google Sheets, you can use =250^(1/3) to calculate the cube root.

For the purposes of this article, we'll use a scientific calculator to work out the cubic root by typing the number 250 and pressing the [∛x] button, to give the following answer:

∛250 ≈ 6.2996052494744

Is 250 a Perfect Cube?

When the cube root of a given number is a whole number, this is called a perfect cube. Perfect cubes are important for many mathematical functions and are used in everything from carpentry through to more advanced topics like physics and astronomy.

If we look at the number 250, we know that the cube root is 6.2996052494744, and since this is not a whole number, we also know that 250 is not a perfect cube.

If you want to learn more about perfect cube numbers we have a list of perfect cubes which covers the first 500 perfect cube numbers.

Is the Cube Root of 250 a Rational or Irrational Number?

Another common question you might find when working with the roots of a number like 250 is whether the given number is rational or irrational. Rational numbers can be written as a fraction and irrational numbers can't.

The quickest way to check if a number is rational or irrational is to determine if it is a perfect cube. If it is, then it's a rational number, but if it is not a perfect cube then it is an irrational number.

We already know that 250 is not a rational number then, because we know it is not a perfect cube.

Rounding the Cube Root of 250

Sometimes when you work with the cube root of 250 you might need to round the answer down to a specific number of decimal places:

10th: ∛250 = 6.3

100th: ∛250 = 6.30

1000th: ∛250 = 6.300

Simplifying the Cube Root of 250

It is possible to simplify the cube root of 250 if the radicand can be made smaller. When that is possible, it is called the cube root of 250 in its simplest radical form.

In this example, the cube root of 250 in its simplest form is:

∛250 = 5∛1

Practice Cube Roots Using Examples

If you want to continue learning about cubic roots, take a look at the random calculations in the sidebar to the right of this blog post.

We have listed a selection of completely random numbers that you can click through and follow the information on calculating the cubic root of that number to help you understand number roots.

Calculate Cube Square Root Problem

Enter your number in box A below and click "Calculate" to work out the cube root of the given number.

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