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Last updated on August 5th, 2025

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Cube Root Of 864

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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 Indian Students
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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
 

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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.
     
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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
 

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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

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 Getting confused with the cube root and square root
 

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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

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Thinking 864 as a perfect cube
 

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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

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Not simplifying the factors properly
 

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Children sometimes forget to simplify the factors properly. To avoid the mistake, students should practice simplifying the factors.
 

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Cube Root of 864 Examples

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Problem 1

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

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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.
 

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Problem 2

Solve for y if y³=864×2.

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 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.
 

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Problem 3

Simplify 864¹/³×864²/³

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 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.
 

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Problem 4

Calculate ∛(864×864​).

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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.
 

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FAQs For Cube Root Of 864

1.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.
 

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2. 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.

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3. 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.

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4.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.

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5.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.

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

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

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

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

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

At BrightChamps in India, 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.

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

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

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Important Glossaries for Cube Root of 864

 

  • 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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About BrightChamps in India

At BrightCHAMPS, we understand algebra goes beyond symbols it’s a pathway to limitless opportunities! Our mission is to help children throughout India master vital math skills, with today’s focus on the Cube Root Of 864 and a special emphasis on grasping cube roots in a way that’s engaging, enjoyable, and easy to follow. Whether your child is calculating the speed of a passing train, keeping track of scores during a cricket match, or managing pocket money for the latest gadgets, mastering algebra builds the confidence needed for everyday life. Our interactive lessons ensure learning is simple and fun. Aware that children in India learn in various ways, we tailor our teaching to each child’s unique style. From the busy markets of Mumbai to the vibrant streets of Delhi, BrightCHAMPS makes math relatable and exciting all over India. Let’s make cube roots a fun part of every child’s math journey!
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