Cube Root of 238328

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, ∛238328 is written as 238328^(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 238328, then y³ can be 238328. Since the cube root of 238328 is an exact value, we can write it as 62.

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 238328. 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 can use the prime factorization method. Since 238328 is a perfect cube, we use this method.

Let's find the cube root of 238328 using the prime factorization method.

Firstly, factorize 238328 into its prime components:

238328 = 2 × 2 × 2 × 7 × 7 × 7 × 11 × 11 × 11

Grouping the prime factors into triples gives: (2 × 2 × 2) × (7 × 7 × 7) × (11 × 11 × 11)

Taking one factor from each group, we get: 2 × 7 × 11 = 154

Therefore, the cube root of 238328 is 154.

• 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: 154^3 = 238328, therefore, 238328 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 which is expressed as (∛).
   
• Rational number: A number is rational if it can be expressed as a fraction or a whole number. The cube root of 238328 is rational because it is an exact whole number.