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708 LearnersLast updated on August 5, 2025
Cube Root of 2
What Is the Cubic Root of 2?
The cube root of 2 is 1.25992104989. The cube root of 2 is expressed as ∛2 in radical form, where the “∛" sign is called the “radical” sign. In exponential form, it is written as (2)⅓. If “m” is the cube root of 2, then, m3=2. Let us find the value of “m”.
Finding the Cubic Root of 2
The Prime Factorization of 2 is 2×1, so, the cube root of 2 is expressed as ∛2 as its simplest radical form. We can find cube root of 2 through another method, named as, Halley’s Method. Let us see how it finds the result.
Cubic Root of 2 By Halley’s 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 ∛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 9.
Step 1: Let a=2. Let us take x as 1, since, 13=1 is the nearest perfect cube which is less than 2.
Step 2: Apply the formula. ∛2≅ 1((13+2×2) / (2(1)3+2))=1.25
Hence, 1.25 is the approximate cubic root of 2.
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Common Mistakes and How to Avoid Them in the Cube Root of 2
below given some mistakes with their solutions:
Mistake 1
Students might guess the cube root by rounding to the nearest number, leading to inaccuracy. For ∛8, the student might mistakenly think the answer is 4, where 23 is the correct answer.
Don’t round off to the nearest number and find cube roots, it is advisable to use proper methods to find cube roots.
Mistake 2
Confusing or misidentifying prime numbers with composite numbers while performing prime factorization to find cube roots.
While prime factorization, make sure you know which numbers are prime and which are not.
Mistake 3
Applying exponent rules incorrectly when finding cube roots.
∛2 is not same as 23. ∛2 = 1.25… and 23=8.
Mistake 4
Students often rely on memorizing rather than understanding concepts of cube root.
Memorizing is not the solution when it comes to complexproblems. So understanding the methods of finding cube roots is advisable.
Mistake 5
Not checking for perfect cubes, like that of 27, before using calculators for approximation.
Try to remember which are the perfect cubes, at least from 1 to 100.
Cube Root of 2 Examples
Problem 1
Find ∛64/ ∛2
∛64/ ∛2
= 4 / 1.25
=3.2
Answer: 3.2
Explanation
We know that the cubic root of 64 is 4, hence dividing 4 by ∛2.
Problem 2
If y = ∛2, find y^3.
y=∛2
⇒ y3= (∛2)3
⇒ y3= 2
Answer: 2
Explanation
(∛2)3=(21/3)3=2. Using this, we found the value of y3.
Problem 3
Subtract ∛2 - ∛1
∛1.25-∛1
= 1.25–1
=0.25
Answer: 0.25
Explanation
We know that the cubic root of 1 is 1, hence subtracting ∛1 from ∛2.
Problem 4
What is ∛(2^6) ?
∛(26)
= ((2)6))1/3
=( 2)2
= 4
Answer: 4
Explanation
We solved and simplified the exponent part first using the fact that, ∛2=(2)⅓, then solved.
Problem 5
Find ∛(2+6)
∛(2+6)
= ∛8
=2
Answer: 2
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 2 Cube Root
1.What is the cube of 2?
2.Is 2 a cube root of 8?
3.What is a cube of √3 ?
4.How to find a cube root?
5.What is the cube root of (-2)?
Important Glossaries for Cube Root of 2
- 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. Ex: 1,2,3,....
- 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.
- Polynomial :It is an algebraic expression made up of variables like “x” and constants, combined using arithmetic operations like 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. It is just near to the exact value.
- 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.
