Cube Root of 50653

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, ∛50653 is written as 50653^(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 50653, then y³ can be 50653. Since 50653 is a perfect cube, the cube root of 50653 is an exact value, which is 37.

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 50653. The common methods we follow to find the cube root are given below:

• Prime factorization method
• Estimation method
• Halley's method

Since 50653 is a perfect cube, we can use the prime factorization method to find its cube root.

Let's find the cube root of 50653 using the prime factorization method.

First, we factorize 50653 into its prime factors:

50653 = 37 × 37 × 37

Since we have three identical factors of 37, the cube root of 50653 is 37.

• 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, 37 × 37 × 37 = 50653, therefore, 50653 is a perfect cube.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 50653^(1/3), ⅓ is the exponent which denotes the cube root of 50653.
   
• Radical sign: The symbol that is used to represent a root is expressed as (∛).
   
• Rational number: A number that can be expressed as a fraction or whole number. The cube root of 50653 is rational because it is a whole number.