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
 

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.
   

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
 

• 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.