116 LearnersLast updated on May 26th, 2025
Cube Root of 906
A number that we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 906 and explain the methods used.
What is the Cube Root of 906?
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓. In exponential form, ∛906 is written as 906(1/3). The cube root is the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 906, then y3 can be 906. Since the cube root of 906 is not an exact value, we can write it as approximately 9.654.
Finding the Cube Root of 906
Finding the cube root of a number involves identifying the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 906. The common methods we follow to find the cube root are given below: -
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
To find the cube root of a non-perfect number, we often follow Halley’s method. Since 906 is not a perfect cube, we use Halley’s method.
Cube Root of 906 by Halley’s Method
Let's find the cube root of 906 using Halley’s method.
The formula is: ∛a ≅ x((x³ + 2a) / (2x³ + a))
where: a = the number for which the cube root is being calculated
x = the nearest perfect cube
Substituting, a = 906; x = 9
∛a ≅ 9((9³ + 2 × 906) / (2 × 9³ + 906))
∛906 ≅ 9((729 + 2 × 906) / (2 × 729 + 906))
∛906 ≅ 9.654
The cube root of 906 is approximately 9.654.
Common Mistakes and How to Avoid Them in the Cube Root of 906
Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes students commonly make and ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Children often try to calculate an exact whole number for the cube root of numbers like 906, which are not perfect cubes. For example, they assume they would get an exact whole number for 906 like they get for 729 (since ∛729 = 9). To avoid this error, remember that some numbers don't have a perfect cube root, that is, the cube root of 906 is approximately 9.654.
Cube Root of 906 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 906 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛906 ≈ 9.654 units
Explanation
To find the side of the cube,
we need to find the cube root of the given volume.
Therefore, the side length of the cube is approximately 9.654 units.
Problem 2
A company manufactures 906 cubic meters of material. Calculate the amount of material left after using 500 cubic meters.
The amount of material left is 406 cubic meters.
Explanation
To find the remaining material,
we need to subtract the used material from the total amount:
906 - 500 = 406 cubic meters.
Problem 3
A bottle holds 906 cubic meters of volume. Another bottle holds a volume of 100 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 1006 cubic meters.
Explanation
Let’s add the volume of both bottles:
906 + 100 = 1006 cubic meters.
Problem 4
When the cube root of 906 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 9.654 = 19.308
The cube of 19.308 ≈ 7197.4
Explanation
When we multiply the cube root of 906 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(800 + 106).
∛(800 + 106) = ∛906 ≈ 9.654
Explanation
Adding 800 and 106 gives us 906.
Then, find the cube root: ∛906 ≈ 9.654.
FAQs on Cube Root of 906
1.Can we find the Cube Root of 906?
2.Why is Cube Root of 906 irrational?
3.Is it possible to get the cube root of 906 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there any formula to find the cube root of a number?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Cube Root of 906?
8.How do technology and digital tools in United Kingdom support learning Algebra and Cube Root of 906?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Cube Root of 906
- Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
- Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example, 2 × 2 × 2 = 8; therefore, 8 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 906(1/3), ⅓ is the exponent which denotes the cube root of 906.
- Radical sign: The symbol that is used to represent a root, which is expressed as (∛).
- Irrational number: Numbers that cannot be put in fractional forms are irrational. For example, the cube root of 906 is irrational because its decimal form goes on continuously without repeating the numbers.
Explore More algebra
Previous to Cube Root of 906
About BrightChamps in United Kingdom
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.
