Last updated on May 26th, 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.
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”.
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.
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.
some mistakes with their solutions given :
Find β250/ β240
β250/ β240
= 6.299 / 6.214
= 6299/6214
=1.014
Answer: 1.014
We found that the cubic root of 240 is 6.214…, hence dividing β250 by β240.
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
We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube.
Subtract β250 - β216, β343-β250
β250-β216= 6.299–6= 0.299
β343-β250 = 7–6.299 = 0.701
Answer: 0.299, 0.701
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.
What is β(250Β²) ?
β(2502) = β62500 = 39.685…
Answer: 39.685
We first found the square value of 250, which is 62500, and then found out the cube root of 62500.
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
Simplified the expression, and found out the cubic root of the result.
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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