Cube Root of 24389

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, ∛24389 is written as 24389^(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 24389, then y³ can be 24389. Since 24389 is a perfect cube, the cube root of 24389 is exactly 29.

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 24389. 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, we can use the prime factorization method. Since 24389 is a perfect cube, this method is effective.

Let's find the cube root of 24389 using the prime factorization method.

We break down 24389 into its prime factors:

24389 = 29 × 29 × 29

Since we have three 29s, the cube root is the number that appears thrice in the factorization.

∛24389 = 29

The cube root of 24389 is exactly 29.

• 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, 29 × 29 × 29 = 24389.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In ∛24389, ⅓ is the exponent which denotes the cube root of 24389.
   
• Radical sign: The symbol that is used to represent a root, expressed as (∛).
   
• Rational number: The numbers that can be expressed as a fraction. For example, the cube root of 24389 is rational because it is 29, which can be represented as 29/1.