Cube Root of 614125

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, ∛614125 is written as 614125^(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 614125, then y³ can be 614125. Since the cube root of 614125 is an exact value, we can write it as exactly 85.

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 614125. 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 number, we often use the prime factorization method. Since 614125 is a perfect cube, we can use this method.

Let's find the cube root of 614125 using the prime factorization method.

First, we find the prime factors of 614125: 614125 = 5 × 5 × 5 × 7 × 7 × 7.

Grouping the factors into triples, we have (5 × 5 × 5) and (7 × 7 × 7).

The cube root is the product of one factor from each group: ∛614125 = 5 × 7 = 35.

The cube root of 614125 is 85.

• 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. A perfect cube always results in a whole number. For example: 5 × 5 × 5 = 125, therefore, 125 is a perfect cube.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 614125^(1/3), ⅓ is the exponent which denotes the cube root of 614125.
   
• Radical sign: The symbol used to represent a root is expressed as (∛).
   
• Factorization: The process of breaking down a number into its prime components. For example, 614125 can be broken down into 5 × 5 × 5 × 7 × 7 × 7.