Cube Root of 474552

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, ∛474552 is written as 474552^(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 474552, then y³ can be 474552. Since the cube root of 474552 is an exact value, we can write it as 78.

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 474552. 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 follow the prime factorization method. Since 474552 is a perfect cube, we can use this method.

Let's find the cube root of 474552 using the prime factorization method.

First, we find the prime factors of 474552: 474552 = 2 × 2 × 2 × 3 × 3 × 3 × 29 × 29 × 29

Grouping the factors into triples, we have: (2 × 2 × 2) × (3 × 3 × 3) × (29 × 29 × 29)

Taking one factor from each group gives us: 2 × 3 × 29 = 78

Therefore, ∛474552 = 78.

• 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: 78 × 78 × 78 = 474552, therefore, 474552 is a perfect cube.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 474552^(1/3), ⅓ is the exponent which denotes the cube root of 474552.
   
• Radical sign: The symbol that is used to represent a root which is expressed as (∛).
   
• Rational number: A number that can be expressed as a fraction or a whole number. The cube root of 474552 is rational because it is 78.