Cube Root of 753571

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, ∛753571 is written as 753571^(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 753571, then y³ can be 753571. The cube root of 753571 is an exact value since 753571 is a perfect cube, and we can write it as 91.

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 753571. 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 number, we often follow the prime factorization method. Since 753571 is a perfect cube, we can use this method.

Let's find the cube root of 753571 using the prime factorization method.

First, we find the prime factors of 753571.

Breaking it down: 753571 = 91 × 91 × 91.

This shows that 91 is multiplied by itself three times to get 753571.

Therefore, the cube root of 753571 is 91.

• 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: 91 × 91 × 91 = 753571, therefore, 753571 is a perfect cube.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a^(1/3), ⅓ is the exponent which denotes the cube root of 'a'.
   
• Radical sign: The symbol that is used to represent a root which is expressed as (∛).
   
• Rational number: Numbers that can be expressed as a fraction of two integers, such as the cube root of 753571, which is a whole number 91.