Our Programs

CodeCHAMPS

Learn More

Table Of Contents

What Is The Cube Root Of 864?

Finding The Cube Root Of 864

Cube Root of 864 using the Halley’s Method

Common Mistakes and How to Avoid Them in Cube Root of 864

Cube Root of 864 Examples

FAQs For Cube Root Of 864

Important Glossaries for Cube Root of 864

Explore More algebra

236 Learners

Last updated on August 5th, 2025

Cube Root Of 864

Q: What is the cube root of 864?

The cube root of 864 is approximately 9.524. This is the number that, when multiplied by itself three times, equals 864.

Q: Is the cube root of 864 a whole number?

No, the cube root of 864 is not a whole number. It is an irrational number, approximately 9.524, and cannot be expressed as an exact integer.

Q: Is the cube root of 864 rational or irrational?

No, the cube root of 864 is an irrational number, as the value of the cube root of 864 is in decimal form.

Q: Can I find the cube root of 864 using exponents?

Yes. We could express 864 this way, 8641/3 = 9.524, the cube root of 864.

Q: How does the cube root of 864 compare to the square root?

The square root of 864 (29.39) is larger than its cube root (9.524) since squaring requires less “shrinking” than cubing.

Q: How does learning Algebra help students in Philippines make better decisions in daily life?

Algebra teaches kids in Philippines to analyze information and predict outcomes, helping them in decisions like saving money, planning schedules, or solving problems.

Q: How can cultural or local activities in Philippines support learning Algebra topics such as Cube Root Of 864?

Traditional games, sports, or market activities popular in Philippines can be used to demonstrate Algebra concepts like Cube Root Of 864, linking learning with familiar experiences.

Q: How do technology and digital tools in Philippines support learning Algebra and Cube Root Of 864?

At BrightChamps in Philippines, we encourage students to use apps and interactive software to demonstrate Algebra’s Cube Root Of 864, allowing students to experiment with problems and see instant feedback for better understanding.

Q: Does learning Algebra support future career opportunities for students in Philippines?

Yes, understanding Algebra helps students in Philippines develop critical thinking and problem-solving skills, which are essential in careers like engineering, finance, data science, and more.

Professor Greenline Explaining Math Concepts

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.

Cube Root Of 864 for Filipino Students

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: 864^1/3

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.

Hey!

Cube Root of 864 Examples

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

Find the volume of a cube with side ∛864.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Okay, lets begin

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.

Well explained 👍

Problem 2

Solve for y if y³=864×2.

Okay, lets begin

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.

Well explained 👍

Problem 3

Simplify 864¹/³×864²/³

Okay, lets begin

864^1/3×864^2/3 = 864¹
864¹=864.

Explanation

When we multiply numbers with the same base, we add the exponents. So, 864^1/3×864^2/3=864¹, which is 864.

Well explained 👍

Problem 4

Calculate ∛(864×864).

Okay, lets begin

∛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.

Well explained 👍

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 Philippines make better decisions in daily life?

7.How can cultural or local activities in Philippines support learning Algebra topics such as Cube Root Of 864?

8.How do technology and digital tools in Philippines support learning Algebra and Cube Root Of 864?

9.Does learning Algebra support future career opportunities for students in Philippines?

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.

About BrightChamps in Philippines

At BrightCHAMPS, we know algebra is more than just numbers it’s a door to countless opportunities! Our mission is to help children across the Philippines develop essential math skills, focusing today on the Cube Root Of 864 with a special emphasis on cube roots in a way that’s lively, fun, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Enchanted Kingdom, keeping score at a local basketball game, or managing their allowance to buy the newest gadgets, mastering algebra gives them the confidence they need for everyday challenges. Our interactive lessons make learning both simple and enjoyable. Recognizing that children in the Philippines learn in many different ways, we tailor our approach to fit each child’s style. From the busy streets of Manila to the beautiful islands of Palawan, BrightCHAMPS brings math to life, making it exciting throughout the Philippines. Let’s make cube roots a fun part of every child’s math adventure!