307 LearnersLast updated on May 26th, 2025
Cube Root of 256
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.
What Is the Cubic Root of 256?
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”.
Finding the Cubic Root of 256
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.
Cubic Root of 256 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 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.
Common Mistakes and How to Avoid Them in the Cubic Root of 256
some common mistakes with their solutions are given below:
Mistake 1
Students might guess the cube root by Trial and Error method, leading to inaccurate results and time wastage.
It is advisable to not use trial and error method for finding cube roots, instead, go for the methods explained above.
Mistake 2
Students can get confused about the fact that cube roots can be rational or irrational. They might think all cube roots are irrational.
The cube roots are rational or irrational depending upon the original number. The β32=3.17… is irrational, whereas β27=3 is rational
Mistake 3
When finding cube roots, students often apply exponent rules incorrectly.
β256 is not same as 2563. The cube root, β256 = 6.34… and the cube of 256, i.e., 2563=16777216.
Mistake 4
Students frequently rely on memorizing rather than understanding concepts of cube root.
Memorizing is not the solution when it comes to complex problems. So understanding the methods of finding cube roots is advisable.
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 300.
Cubic Root of 256 Examples
Problem 1
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
Explanation
Simplified the expression and found the answer.
Problem 2
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
Explanation
Applied the formula and concept of the volume of a cuboid and cube and solved.
Problem 3
Multiply β256 / β216
β256/β216
= 6.34/6
= 1.057
Answer: 1.057
Explanation
We know that the cubic root of 216 is 6, hence dividing β256 by β216.
Problem 4
What is β(256βΆ*ΒΉ/βΆ) ?
β(2566×1/6)
= (256)1/3
= 6.34…
Answer: 6.34
Explanation
We solved and simplified the exponent part first using the fact that, (2566×1/6)=256, then solved.
Problem 5
Find β(256-(-87)).
β(256-(-87))
= β(256+87)
=β343
=7
Answer: 7
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 256 Cube Root
1.Is 256 a perfect square?
2.Is 256 a perfect cube?
3.What is 256 cube root simplified?
4.How to solve 4β256 ?
5.What is the real root of 256?
Important Glossaries for Cubic Root of 256
- Integers - Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.
- Whole numbers - The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity.
- Square root -The square root of a number is a value “y” such that when “y” is multiplied by itself → y × y, the result is the original number.
- Irrational numbers - The numbers which cannot be expressed in the form of “m/n”, where n ≠ 0 and m, n are integers.
- Approximation - Finding out a value which is nearly correct, but not perfectly correct.
- Iterative method - This method is a mathematical process 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.
