Cube 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”.
 

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.
 

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.
 

• 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.