Cube Root of 830584

We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.

In exponential form, ∛830584 is written as 830584^(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 830584, then y³ can be 830584. Since the cube root of 830584 is an exact value, we can write it as 94.

Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 830584. The common methods we follow to find the cube root are given below:

• Prime factorization method
• Approximation method
• Subtraction method
• Halley’s method
   

To find the cube root of a perfect cube, we often follow the prime factorization method. Since 830584 is a perfect cube, we can use this method.

Let's find the cube root of 830584 using the prime factorization method.

Step 1: Find the prime factors of 830584. 830584 = 2 × 2 × 2 × 11 × 11 × 11 × 19 × 19 × 19

Step 2: Group the prime factors into triples. (2 × 2 × 2), (11 × 11 × 11), (19 × 19 × 19)

Step 3: Take one factor from each group and multiply them. Cube root of 830584 = 2 × 11 × 19 = 418

Thus, the cube root of 830584 is 94.

• Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
  
   
• Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. For example: 94 × 94 × 94 = 830584, therefore, 830584 is a perfect cube.
  
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 830584^(1/3), ⅓ is the exponent which denotes the cube root of 830584.
  
   
• Radical sign: The symbol that is used to represent a root is expressed as (∛).
  
   
• Rational number: Numbers that can be expressed as a fraction or ratio are rational. For example, the cube root of 830584 is 94, which is rational.