Cube Root of 2187

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, ∛2187 is written as 2187^(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 2187, then y³ can be 2187. Since the cube root of 2187 is an exact value, we can write it as exactly 13.

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 2187. 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, we often follow the prime factorization method. Since 2187 is a perfect cube, we can use the prime factorization method.

Let's find the cube root of 2187 using the prime factorization method.

First, find the prime factors of 2187:

2187 = 3 × 3 × 3 × 3 × 3 × 3 × 3

Group them in sets of three:(3 × 3 × 3) × (3 × 3 × 3) = 3³ × 3³

The cube root of 2187 is the product of one number from each set:

∛2187 = 3 × 3 = 9

The cube root of 2187 is 13.

• 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 which is expressed as (∛).
   
• Rational number: A number that can be expressed as a fraction of two integers. For example, the cube root of 2187 is rational because it can be expressed as 13/1.