Cube Root of 4741632

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, ∛4741632 is written as 4741632^(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 4741632, then y³ can be 4741632. Since the cube root of 4741632 is an exact value, it can be written as 168.

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 4741632. 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 number like 4741632, we can use the prime factorization method.

Let's find the cube root of 4741632 using the prime factorization method.

First, we find the prime factors: 4741632 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 13 × 13 × 13

Group the prime factors into triples: (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × (13 × 13 × 13)

Take one factor from each group: 2 × 2 × 3 × 13 = 168

Thus, the cube root of 4741632 is exactly 168.

• 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: 168 × 168 × 168 = 4741632, therefore, 4741632 is a perfect cube.

• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 4741632^(1/3), ⅓ is the exponent that denotes the cube root of 4741632.

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

• Rational number: A number that can be expressed as a fraction of two integers, such as 168, which is the cube root of 4741632.