129 LearnersLast updated on May 26th, 2025
Cube Root of 865
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 865 and explain the methods used.
What is the Cube Root of 865?
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, ∛865 is written as 865(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 865, then y3 can be 865. Since the cube root of 865 is not an exact value, we can write it as approximately 9.545.
Finding the Cube Root of 865
Finding the cube root of a number involves identifying the number that must be multiplied three times to reach the target number. Now, we will go through the different ways to find the cube root of 865. 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 865 is not a perfect cube, we use Halley’s method.
Cube Root of 865 by Halley’s Method
Let's find the cube root of 865 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 = 865; x = 9
∛a ≅ 9((93 + 2 × 865) / (2 × 93 + 865))
∛865 ≅ 9((729 + 1730) / (1458 + 865))
∛865 ≅ 9.545
The cube root of 865 is approximately 9.545.
Common Mistakes and How to Avoid Them in the Cube Root of 865
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 the students commonly make and the ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Students often try to calculate an exact whole number for the cube root of numbers like 865, which are not perfect cubes.
For example, they might assume they would get an exact whole number for 865. To avoid this error, memorize that some numbers don't have a perfect cube root, that is, the cube root of 865 is approximately 9.545.
Cube Root of 865 Examples:
Problem 1
Imagine you have a cube-shaped storage box that has a total volume of 865 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛865 ≈ 9.545 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 9.545 units.
Problem 2
A warehouse contains 865 cubic meters of storage capacity. Calculate the remaining capacity after storing 200 cubic meters of goods.
The remaining storage capacity is 665 cubic meters.
Explanation
To find the remaining capacity, we need to subtract the used capacity from the total capacity: 865 - 200 = 665 cubic meters.
Problem 3
A tank holds 865 cubic meters of water. Another tank holds a capacity of 150 cubic meters. What would be the total capacity if both tanks are combined?
The total capacity of the combined tanks is 1015 cubic meters.
Explanation
Let’s add the capacity of both tanks: 865 + 150 = 1015 cubic meters.
Problem 4
When the cube root of 865 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 9.545 ≈ 28.635
The cube of 28.635 ≈ 23473.98
Explanation
When we multiply the cube root of 865 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(432 + 433).
∛(432 + 433) = ∛865 ≈ 9.545
Explanation
As shown in the question ∛(432 + 433), we can simplify that by adding them.
So, 432 + 433 = 865.
Then we use this step: ∛865 ≈ 9.545 to get the answer.
FAQs on Cube Root of 865
1.Can we find the Cube Root of 865?
2.Why is the Cube Root of 865 irrational?
3.Is it possible to get the cube root of 865 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 865
- 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: 3 × 3 × 3 = 27, therefore, 27 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a(1/3), 1/3 is the exponent which denotes the cube root of a.
- Radical sign: The symbol that is used to represent a root, which is expressed as (∛).
- Irrational number: Numbers that cannot be expressed as a simple fraction are irrational. For example, the cube root of 865 is irrational because its decimal form goes on continuously without repeating the numbers.
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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.
