129 LearnersLast updated on May 26th, 2025
Cube Root of 830584
A number 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 830584 and explain the methods used.
What is the Cube Root of 830584?
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, ∛830584 is written as 830584(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 830584, then y3 can be 830584. Since the cube root of 830584 is an exact value, we can write it as 94.
Finding the Cube Root of 830584
Finding the cube root of a number is to identify 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 830584. 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 perfect cube, we often follow the prime factorization method. Since 830584 is a perfect cube, we can use this method.
Cube Root of 830584 by Prime Factorization Method
Let's find the cube root of 830584 using the prime factorization method.
Step 1: Find the prime factors of 830584. 830584 = 2 × 2 × 2 × 11 × 11 × 11 × 19 × 19 × 19
Step 2: Group the prime factors into triples. (2 × 2 × 2), (11 × 11 × 11), (19 × 19 × 19)
Step 3: Take one factor from each group and multiply them. Cube root of 830584 = 2 × 11 × 19 = 418
Thus, the cube root of 830584 is 94.
Common Mistakes and How to Avoid Them in the Cube Root of 830584
Finding the perfect cube of a number without any errors can be a difficult task for the students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:
Mistake 1
Trying to find cube roots for non-perfect cube numbers.
Children sometimes try to calculate a cube root for numbers that are not perfect cubes.
For example, they might mistakenly assume 830584 is not a perfect cube. To avoid this error, verify if a number is a perfect cube before proceeding with calculations.
Cube Root of 830584 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 830584 cubic centimeters. Find the length of one side of the toy equal to its cube root.
Side of the cube = ∛830584 = 94 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 exactly 94 units.
Problem 2
A company manufactures 830584 cubic meters of material. Calculate the amount of material left after using 830000 cubic meters.
The amount of material left is 584 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
830584 - 830000 = 584 cubic meters.
Problem 3
A bottle holds 830584 cubic meters of volume. Another bottle holds a volume of 1000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 831584 cubic meters.
Explanation
Let’s add the volume of both bottles:
830584 + 1000 = 831584 cubic meters.
Problem 4
When the cube root of 830584 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 94 = 188 The cube of 188 = 6,648,752
Explanation
When we multiply the cube root of 830584 by 2, the result is 188. The cube increases significantly because the cube of 188 is much larger than the original volume.
Problem 5
Find ∛(420292+410292).
∛(420292+410292) = ∛830584 = 94
Explanation
As shown in the question ∛(420292+410292), we can simplify that by adding them.
So, 420292 + 410292 = 830584.
Then we use this step: ∛830584 = 94 to get the answer.
FAQs on 830584 Cube Root
1.Can we find the Cube Root of 830584?
2.Why is Cube Root of 830584 considered rational?
3.Is it possible to get the cube root of 830584 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 Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Cube Root of 830584?
8.How do technology and digital tools in Singapore support learning Algebra and Cube Root of 830584?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for Cube Root of 830584
- 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. For example: 94 × 94 × 94 = 830584, therefore, 830584 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 830584(1/3), ⅓ is the exponent which denotes the cube root of 830584.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Rational number: Numbers that can be expressed as a fraction or ratio are rational. For example, the cube root of 830584 is 94, which is rational.
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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.
