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Last updated on November 30th, 2024

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Cube Root of 250

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Foundation
Intermediate
Advance Topics

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.

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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”.
 

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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.
 

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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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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.