Cube Root of 2460375

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, ∛2460375 is written as 2460375^(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 2460375, then y³ can be 2460375. Since the cube root of 2460375 is an exact whole number, we can find it precisely.

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 2460375. 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 2460375 is a perfect cube, we will use this method.

Let's find the cube root of 2460375 using the prime factorization method.

First, perform the prime factorization of 2460375: 2460375 = 3 × 3 × 3 × 5 × 5 × 5 × 7 × 7 × 7

Now, group the prime factors into triples: (3 × 3 × 3) × (5 × 5 × 5) × (7 × 7 × 7)

Each group of three identical factors gives us one factor of the cube root:

Cube root of 2460375 = 3 × 5 × 7 = 105

Thus, the cube root of 2460375 is 105.

• 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, 105 × 105 × 105 = 2460375, therefore, 2460375 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), 1/3 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 that can be expressed as a fraction or whole number. For example, the cube root of 2460375 is rational because it is 105, a whole number.