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649 LearnersLast updated on August 5, 2025
Cube Root of 3
What Is the Cube Root of 3?
The cube root of 3 is 1.44224957031. The cube root of 3 is expressed as ∛3 in radical form, where the “∛" the sign is called the “radical” sign. In exponential form, it is written as (3)⅓. If “m” is the cube root of 3, then, m3=3. Let us find the value of “m”.
Finding the Cube Root of 3
The cube root of 3 is expressed as ∛3 as its simplest radical form. We can find cube root of 3 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cube Root of 3 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 3.
Step 1: Let a=3. Let us take x as 1, since, 13=1 is the nearest perfect cube which is less than 3.
Step 2: Apply the formula. ∛3≅ 1((13+2×3) / (2(1)3+3))= 1.4
Hence, 1.4 is the approximate cubic root of 3.
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Common Mistakes and How to Avoid Them in the Cube Root of 3
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Mistake 1
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 ∛3=1.442… is irrational, whereas ∛8=2 is rational.
Mistake 2
Students forget the concept of cube roots often, by not understanding the definition.
This happens because of uncleared understanding of cube roots and the methods to find it.
Mistake 3
For large non-perfect cubes, students often estimate wrongly and leave it with a wrong result.
Keep the methods of finding cube roots in front whenever attempting large non-perfect cubes.
Mistake 4
Students often 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 64, before using calculators for approximation.
Try to remember which are the perfect cubes, at least from 1 to 100.
Cube Root of 3 Examples
Problem 1
Find ((∛3/ ∛6) × (∛3/ ∛6) × (∛3/ ∛6)) + (((∛3/ ∛6) × (∛3/ ∛6) × (∛3/ ∛6))
((∛3/ ∛6) × (∛3/ ∛6) × (∛3/ ∛6)) +((∛3/ ∛6) × (∛3/ ∛6) × (∛3/ ∛6))
= ((∛3× ∛3× ∛3) / (∛6× ∛6× ∛6)) + ((∛3× ∛3× ∛3) / (∛6× ∛6× ∛6))
=((3)⅓)3/ ((6)⅓)3 + ((3)⅓)3/ ((6)⅓)
=3/6 + 3/6
= 1/2 + 1/2
=1
Answer: 1
Explanation
We solved and simplified the exponent part first using the fact that, ∛3=(3)⅓ and ∛6=(6)⅓ , then solved.
Problem 2
If y = ∛3, find y³.
y=∛3
⇒ y3= (∛3)3
⇒ y3= 3
Answer: 3
Explanation
(∛3)3=(31/3)3=3. Using this, we found the value of y3.
Problem 3
Subtract ∛3 + ∛27 + √9 + √27
∛3 + ∛27 + √9 + √27
= 1.442 + 3 + 3 + 5.196
= 12.638
Answer: 12.638
Explanation
We know that the cubic root of 27 is 3, the square root of 9 is ±3, and the square root of 27 is ±5.196 hence applying these solved the problem
Problem 4
What is ∛(3⁶) + ∛(3⁹) ?
∛(36) + ∛(39)
= ((3)6))1/3 + ((3)9)1/3
=(3)2 + (3)3
= 9 + 27
= 36
Answer: 36
Explanation
We solved and simplified the exponent part first using the fact that, ∛3=(3)⅓, then solved.
Problem 5
Find ∛(3+5)).
Solution:
∛(3+5)
= ∛8
= 2
Answer: 2
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 3 Cube Root
1.How to calculate ∛ ?
2.How to find the cube of 3?
3.Can you simplify ∛3?
4.Is √3 possible?
5.Is √3 real?
Important Glossaries for Cube Root of 3
- 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.
- Polynomial - It is an algebraic expression made up of variables like “x” and constants, combined using 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.
- 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.
