Cube Root of 250
2026-02-28 09:15 Diff
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Last updated on August 5, 2025

The cube root of 250 is the value which, when multiplied by itself three times (cubed), gives the original number 250. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, creating unique digital art etc.

What Is the Cubic Root of 250?

The cube root of 250 is 6.29960524947. The cube root of 250 is expressed as ∛250 in radical form, where the “ ∛ “  sign" is called the “radical” sign. In exponential form, it is written as (250)1/3.  If “m” is the cube root of 250, then, m3=250.  Let us find the value of “m”.
 

Finding the Cube Root of 250

The cube root of 250 is expressed as 5∛2 as its simplest radical form, since


 250 = 5×5×5×2


∛250 = ∛(5×5×5×2)


Group together three same factors at a time and put the remaining factor under ∛ .


∛250= 5∛2 


 We can find cube roots of 250 through a method, named as, Halley’s Method. Let us see how it finds the result.
 

Cube Root of 250 By Halley’s Method

Now, what is Halley’s Method? It is an iterative method for finding cube roots of a given number N, such that, x3=N, where this method approximates the value of “x”.


Formula is ∛a≅ x((x3+2a) / (2x3+a)), where 


a=given number whose cube root you are going to find


x=integer guess for the cubic root


Let us apply Halley’s method on the given number 250.


Step 1: Let a=250. Let us take x as 6, since 63=216 is the nearest perfect cube which is less than 250.


Step 2: Apply the formula.  ∛250≅ 6((63+2×250) / (2(6)3+250))= 6.29…


Hence, 6.29… is the approximate cubic root of 250.
 

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Problem 1

Find ∛250/ ∛240

Okay, lets begin

 ∛250/ ∛240

= 6.299 / 6.214

= 6299/6214

=1.014


Answer: 1.014
 

Explanation

We found that the cubic root of 240 is 6.214…, hence dividing  ∛250 by ∛240.
 

Well explained 👍

Problem 2

The Volume of a cube is 250 cubic centimeters, find the length of one side of the cube.

Okay, lets begin

We know that, (side of a cube)3=Volume of a cube


⇒side of the cube =  ∛(Volume of the cube)


⇒side of the cube = ∛250


⇒ side of the cube = 6.299 cm


Answer: 6.299 cm
 

Explanation

We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube.
 

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Problem 3

Subtract ∛250 - ∛216, ∛343-∛250

Okay, lets begin

 ∛250-∛216= 6.299–6= 0.299


∛343-∛250 = 7–6.299 = 0.701


Answer:  0.299, 0.701
 

Explanation

We know that the cubic root of 216 is 6, hence subtracting  ∛216 from ∛250. Applying the same for the next one, we know that the cubic root of 343 is 7, hence subtracting ∛250 from ∛343.
 

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Problem 4

What is ∛(250²) ?

Okay, lets begin

 ∛(2502) = ∛62500 = 39.685… 


Answer: 39.685
 

Explanation

We first found the square value of 250, which is 62500, and then found out the cube root of 62500.
 

Well explained 👍

Problem 5

Find ∛((250+93)×(250+262)).

Okay, lets begin

 ∛((250+93)×(250+262))

= ∛(343×512)

=∛((7)3 × (8)3)

=∛73  ×  ∛83

= 7 × 8

=56


Answer: 56
 

Explanation

Simplified the expression, and found out the cubic root of the result. 
 

Well explained 👍

FAQs on 250 Cube Root

1.What is the simplest form of 3√250 ?

 3√250 = 3√(5×5×5×2) = 3×5√10 =15√10.
 

2.What number cube is 250?

: (5∛2)3 = 250. Hence, 5∛2, when cubed, gives 250.

3.Is 250 a square root?

4.How to find the cube root of 255?

The cube root of 255 is the value which, when multiplied by itself three times (cubed), gives the original number, 255. So, cube roots can be found through prime factorization method or Halley’s method. The value of ∛255 is 6.34…

5.Is the ∛250 irrational?

Yes, ∛250=6.29… is an irrational number, since it cannot be expressed in the form p/q, where p and q are integers and q≠0.
 

Important Glossaries for Cube Root of 250

  • Irrational Numbers - Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 
  • Whole numbers - The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. These cannot be in fractional or decimal form. 
  • Square root -The square root of a number is a value, which, on multiplication by itself, gives the original number, such that √x = y, where y×y = x.
  • Polynomial - It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.
  • Approximation - Finding out a value which is nearly correct, but not perfectly correct, as if the approximate value is just near and close to the original value.
  • Iterative method - This method is a process, used in mathematics, which uses an initial value to generate further and step-by-step sequence of solutions for a problem.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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: He loves to play the quiz with kids through algebra to make kids love it.