Cube Root of 175616

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, ∛175616 is written as 175616^(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 175616, then y³ can be 175616. The cube root of 175616 is an exact value, which is 56.

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 175616. 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 often follow the prime factorization method. Since 175616 is a perfect cube, we use this method.

Let's find the cube root of 175616 using the prime factorization method.

First, we factorize 175616 into its prime factors: 175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7

Grouping the factors in triples: (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (7 × 7 × 7)

Each group of three identical factors corresponds to a factor of the cube root: ∛175616 = 2 × 2 × 2 × 7 = 56

The cube root of 175616 is 56.

• 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, 56 × 56 × 56 = 175616.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 175616^(1/3), ⅓ is the exponent which denotes the cube root of 175616.
   
• Radical sign: The symbol that is used to represent a root which is expressed as (∛).
   
• Rational number: Numbers that can be expressed as a fraction or a whole number. The cube root of 175616 is rational because it results in a whole number.