Cube Root of 35937

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, ∛35937 is written as 35937^(1/3). The cube root is just the opposite operation of finding the cube of a number. For example, assume ‘y’ is the cube root of 35937, then y³ can be 35937. Since the cube root of 35937 is an exact value, it is 33.

Finding the cube root of a number involves identifying the number that must be multiplied three times to result in the target number. Now, we will go through the different ways to find the cube root of 35937. The common methods we follow to find the cube root are given below:

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

Since 35937 is a perfect cube, we can use the prime factorization method to find its cube root.

Let's find the cube root of 35937 using the prime factorization method.

First, we factorize 35937 into its prime factors:

35937 = 3 × 3 × 3 × 11 × 11 × 11

Grouping the prime factors into triples, we have:

(3 × 3 × 3) and (11 × 11 × 11)

The cube root is the product of one factor from each group: ∛35937 = 3 × 11 = 33

The cube root of 35937 is 33.

• 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 (∛).
   
• Prime factorization: A method of breaking down a number into its prime factors, which can be useful in determining whether a number is a perfect cube.