262 LearnersLast updated on May 26th, 2025
Cube Root of 250
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 β250 in radical form, where the “ β “ 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 5β2 as its simplest radical form, since
250 = 5×5×5×2
β250 = β(5×5×5×2)
Group together three same factors at a time and put the remaining factor under β .
β250= 5β2
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 Halleyβs 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 βa≅ 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. β250≅ 6((63+2×250) / (2(6)3+250))= 6.29…
Hence, 6.29… is the approximate cubic root of 250.
Common Mistakes and How to Avoid Them in the Cube Root of 250
some mistakes with their solutions given :
Mistake 1
Children get confused with the concept of cube root with that of square root.
The Cube root of 250 is β250, and the square root of 250 is √250. Understand the definition of Cube roots and square roots.
Mistake 2
Misidentifying prime numbers with composite numbers while doing prime factorization to find cube roots.
While prime factorization, make sure you know which numbers are prime and which are not. Have a clear vision on prime numbers and composite numbers before applying the Prime Factorization method.
Mistake 3
Applying exponent rules incorrectly when finding cube roots.
β250 is not same as 2503. β250 =6.29… and 2503=15625000.
Mistake 4
Students often calculate mentally the value of cube roots.
Students can use Prime factorization method or Halley’s method to find out the approximate value for cube roots.
Mistake 5
Not checking for perfect cubes, like that of 216, before using calculators for approximation.
Try to remember which are the perfect cubes, at least from 1 to 1000.
Cube Root of 250 Examples
Problem 1
Find β250/ β240
β250/ β240
= 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 β250 by β240.
Problem 2
The Volume of a cube is 250 cubic centimeters, find the length of one side of the cube.
We know that, (side of a cube)3=Volume of a cube
⇒side of the cube = β(Volume of the cube)
⇒side of the cube = β250
⇒ 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.
Problem 3
Subtract β250 - β216, β343-β250
β250-β216= 6.299–6= 0.299
β343-β250 = 7–6.299 = 0.701
Answer: 0.299, 0.701
Explanation
We know that the cubic root of 216 is 6, hence subtracting β216 from β250. Applying the same for the next one, we know that the cubic root of 343 is 7, hence subtracting β250 from β343.
Problem 4
What is β(250Β²) ?
β(2502) = β62500 = 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.
Problem 5
Find β((250+93)Γ(250+262)).
β((250+93)×(250+262))
= β(343×512)
=β((7)3 × (8)3)
=β73 × β83
= 7 × 8
=56
Answer: 56
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 250 Cube Root
1.What is the simplest form of 3β250 ?
2.What number cube is 250?
3.Is 250 a square root?
4.How to find the cube root of 255?
5.Is the β250 irrational?
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
