Cube Root of 1404928

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, ∛1404928 is written as 1404928^(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 1404928, then y³ can be 1404928. Since 1404928 is a perfect cube, its cube root is exactly 112.

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 1404928. The common methods we follow to find the cube root are given below:

- Prime factorization method

- Estimation method

- Halley’s method

Since 1404928 is a perfect cube, we can use the prime factorization method to find its cube root.

Let's find the cube root of 1404928 using the prime factorization method. The prime factorization of 1404928 is: 1404928 = 2¹⁰ × 7³

To find the cube root, we take the cube root of each factor: ∛(2^10 × 7^3) = 2^(10/3) × 7^(3/3)

Simplifying: = 2^3 × 7 = 8 × 7 = 56

Therefore, the cube root of 1404928 is 112.

• 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, 4 × 4 × 4 = 64, therefore, 64 is a perfect cube.

• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. For example, x^(1/3) is the cube root of x.

• Radical sign: The symbol used to represent a root is expressed as (∛).

• Prime factorization: This is a method of breaking down a number into its prime factors, useful for finding the cube root of perfect cubes.