Cube Root of 9261000

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, ∛9261000 is written as 9261000^(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 9261000, then y³ can be 9261000. Since 9261000 is a perfect cube, the cube root of 9261000 is exactly 210.

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 9261000. The common methods we follow to find the cube root are given below:

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

Since 9261000 is a perfect cube, we can use the prime factorization method to find the cube root efficiently.

Let's find the cube root of 9261000 using the prime factorization method.

First, we find the prime factors of 9261000.

9261000 = 2 × 2 × 2 × 3 × 3 × 5 × 5 × 7 × 7 × 7 × 10 × 10 × 10

Grouping the factors in triples, we get: (2 × 2 × 2), (3 × 3), (5 × 5), (7 × 7 × 7), (10 × 10 × 10)

The cube root of 9261000 is: 2 × 3 × 5 × 7 × 10 = 210

Therefore, the cube root of 9261000 is 210.

• 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: 210 × 210 × 210 = 9261000, therefore, 9261000 is a perfect cube.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 9261000^(1/3), ⅓ is the exponent which denotes the cube root of 9261000.
   
• Radical sign: The symbol that is used to represent a root which is expressed as (∛). Prime factorization: A method of expressing a number as the product of its prime factors, used to find cube roots of perfect cubes efficiently.