117 LearnersLast updated on May 26th, 2025
Cube Root of 6859
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 6859 and explain the methods used.
What is the Cube Root of 6859?
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, ∛6859 is written as 6859(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 6859, then y3 can be 6859. Since the cube root of 6859 is an exact value, it is 19.
Finding the Cube Root of 6859
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 6859. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Direct calculation method
- Estimation method
To find the cube root of a perfect cube, we can use the prime factorization method or direct calculation method since 6859 is a perfect cube.
Cube Root of 6859 by Prime Factorization Method
Let's find the cube root of 6859 using the prime factorization method. First, we find the prime factors of 6859: 6859 = 19 × 19 × 19 Since we have three identical factors of 19, the cube root of 6859 is 19.
Common Mistakes and How to Avoid Them in the Cube Root of 6859
Finding the cube root 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 non-perfect cube roots for perfect cube numbers.
Children sometimes try to calculate an approximate value for the cube root of numbers like 6859, which is a perfect cube.
For example: They might assume that they would need to use approximation methods. To avoid this error, memorize that some numbers have an exact cube root, that is, the cube root of 6859 is exactly 19.
Cube Root of 6859 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 6859 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛6859 = 19 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 19 units.
Problem 2
A company manufactures 6859 cubic meters of material. Calculate the amount of material left after using 3000 cubic meters.
The amount of material left is 3859 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
6859 - 3000 = 3859 cubic meters.
Problem 3
A bottle holds 6859 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 7859 cubic meters.
Explanation
Explanation: Let’s add the volume of both bottles:
6859 + 1000 = 7859 cubic meters.
Problem 4
When the cube root of 6859 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 19 = 38 The cube of 38 = 54872
Explanation
When we multiply the cube root of 6859 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(1000+5859).
∛(1000+5859) = ∛6859 = 19
Explanation
As shown in the question ∛(1000+5859), we can simplify that by adding them.
So, 1000 + 5859 = 6859.
Then we use this step: ∛6859 = 19 to get the answer.
FAQs on 6859 Cube Root
1.Can we find the Cube Root of 6859?
2.Why is the Cube Root of 6859 rational?
3.Is it possible to get the cube root of 6859 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?
Important Glossaries for Cube Root of 6859
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: 19 × 19 × 19 = 6859, therefore, 6859 is a perfect cube.
Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 6859(1/3), ⅓ is the exponent which denotes the cube root of 6859.
Radical sign: The symbol that is used to represent a root which is expressed as (∛).
Rational number: Numbers that can be expressed as a fraction or whole number. The cube root of 6859 is rational because it is exactly 19.
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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.
