Cube Root of 19683

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, ∛19683 is written as 19683^(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 19683, then y³ can be 19683. Since 19683 is a perfect cube, its cube root is exactly 27.

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 19683. The common methods we follow to find the cube root are given below:

• Prime factorization method
   
• Approximation method
   
• Subtraction method
   
• Halley’s method

For 19683, which is a perfect cube, one of the simplest methods is the prime factorization method.

Let's find the cube root of 19683 using the prime factorization method. First, find the prime factors of 19683:

19683 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = 3⁹

To find the cube root, group the factors into triples: (3 × 3 × 3) × (3 × 3 × 3) × (3 × 3 × 3)

Each group gives a factor of 3, and there are three groups.

Thus, the cube root of 19683 is 3 × 3 × 3 = 27.

• 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, 3 × 3 × 3 = 27, therefore, 27 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 is expressed as (∛).

• Rational number: A number that can be expressed as a fraction or whole number. The cube root of 19683 is rational because it is a whole number.