Last updated on November 30th, 2024
The cube root of 256 is the value which, when multiplied by itself three times (cubed), gives the original number 256. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, designing structures, density and mass, used in day-to-day mathematics like exponents, etc.
The cube root of 256 is 6.34960420787. The cube root of 256 is expressed as ∛256 in radical form, where the “ ∛ “ sign is called the “radical” sign. In exponential form, it is written as (256)1/3. If “m” is the cube root of 256, then, m3=256. Let us find the value of “m”.
The cube root of 256 is expressed as 4∛4 as its simplest radical form, since
256 = 2×2×2×2×2×2×2×2
∛256 = ∛(2×2×2×2×2×2×2×2)
Group together three same factors at a time and put the remaining factor under ∛ .
∛256= 4∛4
We can find cube root of 256 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 256.
Step 1: Let a=256. Let us take x as 6, since, 63=216 is the nearest perfect cube which is less than 256.
Step 2: Apply the formula. ∛256≅ 6((63+2×256) / (2(6)3+256))= 6.34
Hence, 6.34 is the approximate cubic root of 256.
Find ((∛343/ ∛256) × (∛512/ ∛256)) / ((∛216 / ∛256) × (∛125 / ∛256))
The length, breadth, and height of a cuboid is 9 unit, 4 unit, and 8 cm respectively. To find its volume, also find the measure of a side of a cube, whose volume is 256 cubic units.
Multiply ∛256 / ∛216
What is ∛(256⁶*¹/⁶) ?
Find ∛(256-(-87)).
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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