Cube Root of 74088000

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, ∛74088000 is written as 74088000^(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 74088000, then y³ can be 74088000. The cube root of 74088000 is an exact value, which is 420.

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 74088000. The common methods we follow to find the cube root are given below:

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

Since 74088000 is a perfect cube, we can use the prime factorization method or estimation method.

Let's find the cube root of 74088000 using the prime factorization method.

First, we factorize 74088000 into its prime factors: 74088000 = 2⁶ × 3² × 5³ × 7³

To find the cube root, we take the cube root of each factor: ∛(2⁶ × 3² × 5³ × 7³)

= 2^(6/3) × 3^(2/3) × 5^(3/3) × 7^(3/3)

2² × 3^(2/3) × 5 × 7

4 × (3^(2/3)) × 5 × 7

4 × 3 × 5 × 7 = 420

The cube root of 74088000 is 420.

• 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: 5 × 5 × 5 = 125, therefore, 125 is a perfect cube.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 74088000^(1/3), ⅓ is the exponent which denotes the cube root.
   
• Radical sign: The symbol that is used to represent a root is expressed as (∛).
   
• Prime factorization: A method used to express a number as a product of its prime factors, particularly helpful in finding cube roots of perfect cubes.