Cube Root of 592704

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, ∛592704 is written as 592704^(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 592704, then y³ can be 592704. Since the cube root of 592704 is an exact value, it can be written as 84.

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 592704. 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 use the prime factorization method. Since 592704 is a perfect cube, we use the prime factorization method.

Let's find the cube root of 592704 using the prime factorization method.

First, we express 592704 as a product of its prime factors: 592704 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7 × 7

Now, group the factors in triples: (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × (7 × 7 × 7)

Each group of three identical numbers represents the cube of a number.

Thus, the cube root of 592704 is: ∛592704 = 2 × 2 × 3 × 7 = 84

The cube root of 592704 is 84.

• 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: 2 × 2 × 2 = 8, therefore, 8 is a perfect cube.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 592704^(1/3), ⅓ is the exponent which denotes the cube root of 592704.
   
• 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 ratio of two integers. The cube root of 592704 is rational because it equals 84.