Cube Root of 91125

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, ∛91125 is written as (91125^{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 91125, then (y³) can be 91125. The cube root of 91125 is 45.

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 91125. The common methods we follow to find the cube root are given below:

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

Since 91125 is a perfect cube, we can use the prime factorization method to find its cube root efficiently.

Let's find the cube root of 91125 using the prime factorization method.

First, we find the prime factors of 91125: 91125 = 3 × 3 × 3 × 5 × 5 × 5 × 11 × 11 × 11

Group the prime factors in triples: (3 × 3 × 3), (5 × 5 × 5), (11 × 11 × 11)

The cube root is the product of one factor from each group: 3 × 5 × 11 = 45

Therefore, the cube root of 91125 is 45.

• 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: 3 × 3 × 3 = 27, therefore, 27 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}), ⅓ is the exponent, which denotes the cube root of a.

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

• Rational number: The numbers that can be expressed as a fraction of two integers are rational. For example, 45 is rational because it can be expressed as 45/1.