Last updated on May 26th, 2025
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 β256 in radical form, where the “ β “ 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 4β4 as its simplest radical form, since
256 = 2×2×2×2×2×2×2×2
β256 = β(2×2×2×2×2×2×2×2)
Group together three same factors at a time and put the remaining factor under β .
β256= 4β4
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 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 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. β256≅ 6((63+2×256) / (2(6)3+256))= 6.34
Hence, 6.34 is the approximate cubic root of 256.
some common mistakes with their solutions are given below:
Find ((β343/ β256) Γ (β512/ β256)) / ((β216 / β256) Γ (β125 / β256))
((β343/ β256) × (β512/ β256)) / ((β216 / β256) × (β125 / β256))
= (β343× β512) / (β216× β125)
=(7× 8)/ (6× 5)
=56/30
=28/15
Answer: 28/15
Simplified the expression and found the answer.
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.
Volume of a cuboid = length × breadth × height = 9 × 4 × 8 cubic units = 288 cubic units.
Given, Volume of a cube = 256 cubic units
⇒ side × side × side = 256 cubic units
⇒ side = β256
⇒ side = 6.34 units
Answer: Volume of the cuboid = 288 cubic units
Side length of the cube = 6.34 units
Applied the formula and concept of the volume of a cuboid and cube and solved.
Multiply β256 / β216
β256/β216
= 6.34/6
= 1.057
Answer: 1.057
We know that the cubic root of 216 is 6, hence dividing β256 by β216.
What is β(256βΆ*ΒΉ/βΆ) ?
β(2566×1/6)
= (256)1/3
= 6.34…
Answer: 6.34
We solved and simplified the exponent part first using the fact that, (2566×1/6)=256, then solved.
Find β(256-(-87)).
β(256-(-87))
= β(256+87)
=β343
=7
Answer: 7
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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