BrightChamps Logo
Hamburger Menu Icon for BrightChamps Website Navigation
Login
Creative Math Ideas Image
Live Math Learners Count Icon150 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Cube Root Of 864

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 UK Students
Professor Greenline from BrightChamps

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
 

Professor Greenline from BrightChamps

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.
     
Professor Greenline from BrightChamps

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
 

Max Pointing Out Common Math Mistakes

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

 Getting confused with the cube root and square root
 

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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.

Max from BrightChamps Saying "Hey"

Cube Root of 864 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Find the volume of a cube with side ∛864​.

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

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

Solve for y if y³=864×2.

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

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Simplify 864¹/³×864²/³

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

 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.
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

Calculate ∛(864×864​).

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

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs For Cube Root Of 864

1.What is the cube root of 864?

Math FAQ Answers Dropdown Arrow

2. Is the cube root of 864 a whole number?

Math FAQ Answers Dropdown Arrow

3. Is the cube root of 864 rational or irrational?

Math FAQ Answers Dropdown Arrow

4.Can I find the cube root of 864 using exponents?

Math FAQ Answers Dropdown Arrow

5.How does the cube root of 864 compare to the square root?

Math FAQ Answers Dropdown Arrow

6.How does learning Algebra help students in United Kingdom make better decisions in daily life?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

About BrightChamps in United Kingdom

At BrightChamps, we believe algebra is far more than mere symbols—it opens the door to countless opportunities! Our mission is to help children throughout the United Kingdom build strong math skills, with today’s focus on the Cube Root Of 864, placing special emphasis on understanding cube roots—in an engaging, enjoyable, and accessible way. Whether your child is working out how fast a roller coaster moves at Alton Towers, keeping score at a local football match, or managing their pocket money for the latest gadgets, mastering algebra gives them confidence for everyday situations. Our interactive lessons are designed to be fun and straightforward. Recognizing that children in the UK learn differently, we adapt our teaching to each child’s individual style. From the bustling streets of London to the picturesque coasts of Cornwall, BrightChamps makes math come alive, exciting learners all over the UK. Let’s make cube roots an enjoyable part of every child’s math journey!
INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom