247 LearnersLast updated on May 26th, 2025
Cube Root of 6
The cube root of 6 is the value that, when multiplied by itself three times (cubed), gives the original number 6. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.
What Is the Cube Root of 6?
The cube root of 6 is 1.81712059283. The cube root of 6 is expressed as ∛6 in radical form, where the “ ∛ “ sign" is called the “radical” sign. In exponential form, it is written as (6)1/3. If “m” is the cube root of 6, then, m3=6. Let us find the value of “m”.
Finding the Cube Root of 6
The cube root of 6 is expressed as ∛6 as its simplest radical form. We can find cube root of 6 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cube Root of 6 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 6.
Step 1: Let a=6. Let us take x as 1, since, 13=1 is the nearest perfect cube which is less than 6.
Step 2: Apply the formula. ∛6≅ 1((13+2×6) / (2(1)3+6))=1.625. Hence, 1.625 is the approximate cubic root of 6.
Common Mistakes and How to Avoid Them in the Cube Root of 6
Misconceptions or mistakes are common, so let us see how we can avoid those from happening. Here are some misconceptions listed below with their respective solutions.
Mistake 1
For arithmetic operations inside a cube root radical, like that of ∛(6+2), students often write it as ∛6+2, where the meaning changes.
It is advisable to put brackets after cube root radical for a better understanding of any arithmetic operations.
Cube Root of 6 Examples
Problem 1
The length, breadth, and height of a cuboid is 2 units, 2.5 units, and 2.8 units respectively. To find its volume, also find the measure of a side of a cube whose volume is 6 cubic units.
Volume of a cuboid = length × breadth × height = 2 × 2.5 × 2.8 cubic units = 14 cubic units.
Given, Volume of a cube = 6 cubic units
⇒ side × side × side = 6 cubic units
⇒ side = ∛6
⇒ side = 1.817 units
Answer: Volume of the cuboid = 14 cubic units
Side length of the cube = 1.817 units
Explanation
Applied the formula and concept of the volume of a cuboid and cube and solved.
Problem 2
If y = ∛6, find y³/ y⁶
y=∛6
⇒ y3/y6= (∛6)3 / (∛6)6
⇒ y3/y6= 6/ (6)2= 1/6
Answer: 1/6
Explanation
(∛6)3=(61/3)3=6, and (∛6)6=(61/3)6=(6)2. Using this, we found the value of y3/y6.
Problem 3
Multiply ∛6 × ∛8 × ∛27
∛6×∛8× ∛27
= 1.817×2×3
= 10.902.
Answer: 10.902
Explanation
We know that the cubic root of 27 is 3 and that of 8 is 2, hence multiplying.
Problem 4
What is ∛(6⁶)²?
∛(66)2
= (((6)6)2)1/3
=(6)12/3
= (6)4
=1296
Answer: 1296
Explanation
We solved and simplified the exponent part first using the fact that, ∛6=(6)⅓, then solved.
Problem 5
Find ∛6 / 18.17.
(∛6) / 18.17
= 1.817 /18.17
=0.1
Answer: 0.1
Explanation
Simplified the expression, and found out the result.
FAQs on 6 Cube Root
1. Is 216, the cube of 6?
2.What is a cube root of 7?
3.Is 6 a perfect cube?
4.How to solve ∛5 ?
5.How do you simplify ∛6?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Cube Root of 6?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Cube Root of 6?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for Cube Root of 6
- Irrational Numbers - Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers.
- 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.
