242 LearnersLast updated on August 5th, 2025
Cube Root Of 864
A cube root of a number is a value, when it is multiplied by itself three times, gives the original number. Imagine you have a cube (box) with the known volume. The cube root helps us determine the length of one side of the box.
What Is The Cube Root Of 864?
The cube root of 864 is the number which, when multiplied three times, we get a number that is equal to 864. Let’s explore some steps and methods to calculate the cube root of 864.
The cube root of 864: ∛864 = 9.524
The exponential form of the cube root of 864: 8641/3
The radical form of the cube root of 864: ∛864
Finding The Cube Root Of 864
To find the cube root of 864, we use the following methods:
- Prime factorization
- Approximation method
- Long division
- Subtraction method
- Halley’s method is used for those numbers which are not perfect cubes.
Cube Root of 864 using the Halley’s Method
We use the below formula to find the cube root using Halley’s Method;
∛a ≅ x((x3+2a) / (2x3+a))
In the formula;
a = given number, 864
x = an approximate number close to the cube root of the number, 864: 93= 729
Let’s apply the formula and find the Cube Root:
A = 864, for the approximate method we choose, x = 9, it is the nearest cube (93= 729).
Now apply the formula;
∛a ≅ x((x3+2a) / (2x3+a))
∛864 ≅ 9((93+2 × 864) / (2 × 93+864)) = 9.524
Hence, the approximate cube of 864 ≅ 9.524
Common Mistakes and How to Avoid Them in Cube Root of 864
While learning about cube roots, children making mistakes is common, so to avoid a few mistakes that are likely to happen, below are a few mistakes and how to avoid these:
Mistake 1
Getting confused with the cube root and square root
Students sometimes multiply the same number twice instead of thrice, which makes it a square root and not a cube root. Because of this, improper results are to be found. To avoid these, students should practice square roots and cube roots regularly.
Mistake 2
Thinking 864 as a perfect cube
Children sometimes think that 864 is a perfect cube, as it ends with 64 children thinking it as a perfect cube. Which gives improper results, to avoid this mistake students should practice.
Mistake 3
Not simplifying the factors properly
Children sometimes forget to simplify the factors properly. To avoid the mistake, students should practice simplifying the factors.
Cube Root of 864 Examples
Problem 1
Find the volume of a cube with side ∛864.
Side(S) = ∛864.
Volume = S3
Volume = 9.5243 = 864 units.
Explanation
To find a cube’s volume, multiply the side length by itself three times. Here, 9.5453=864 units.
Problem 2
Solve for y if y³=864×2.
y3 =864×2 = 1728
y = ∛1728=12.
Explanation
First, multiply 864×2=1728. Then, find the cube root of 1728, which means the number that, when multiplied by itself three times, equals 1728.
Problem 3
Simplify 864¹/³×864²/³
8641/3×8642/3 = 8641
8641=864.
Explanation
When we multiply numbers with the same base, we add the exponents. So, 8641/3×8642/3=8641, which is 864.
Problem 4
Calculate ∛(864×864).
∛864 = 9.524
9.524 × 9.524 = 90.70
Explanation
To find this, we approximate each cube root as about 9.545. Then, we multiply 9.545 by 9.545 to get 91.
FAQs For Cube Root Of 864
1.What is the cube root of 864?
2. Is the cube root of 864 a whole number?
3. Is the cube root of 864 rational or irrational?
4.Can I find the cube root of 864 using exponents?
5.How does the cube root of 864 compare to the square root?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Cube Root Of 864?
8.How do technology and digital tools in India support learning Algebra and Cube Root Of 864?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for Cube Root of 864
- Whole numbers — The whole numbers are the set of numbers that consists of natural numbers and zero. Example: 0, 1, 2, 3………..
- Square root —A number’s square root is considered a number that when it is multiplied by itself results in the same number.Example: √4 is 2.
- Exponent: It is a number which represents how many times a base number should be multiplied.Example: 42=4 × 4 = 16
- Irrational number: The number that cannot be expressed in the form of fraction. Example: √2 is an irrational number.
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