Cube Root of 166375

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, ∛166375 is written as 166375^(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 166375, then y³ can be 166375. The cube root of 166375 is an exact value, 55, since 166375 is a perfect cube.

Finding the cube root of a number involves identifying 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 166375. The common methods we follow to find the cube root are given below:

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

Since 166375 is a perfect cube, the prime factorization method is suitable for finding its cube root.

Let's find the cube root of 166375 using the prime factorization method.

First, factorize 166375 into its prime factors:

166375 = 5 × 5 × 5 × 11 × 11 × 11 2.

Group the factors into triples: (5 × 5 × 5) and (11 × 11 × 11) 3.

Take one factor from each group: 5 and 11 4.

Multiply the factors: 5 × 11 = 55

The cube root of 166375 is 55.

• 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: 5 × 5 × 5 = 125, therefore, 125 is a perfect cube.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 166375^(1/3), ⅓ is the exponent which denotes the cube root of 166375.
   
• Radical sign: The symbol that is used to represent a root is expressed as (∛).
   
• Prime factorization: A method of expressing a number as the product of its prime factors. This method is particularly useful for finding cube roots of perfect cubes.