Cube Root Of 21

The cube root can be classified into two categories: perfect cubes and non-perfect cubes. For example, the cube root of 27 is 3 which is a whole number, making it a perfect cube. However, the cube root of 21 is not a whole number. The cube root of 21 is approximately 2.759.

The cube root of 21 is represented using the radical sign as ∛21, and can also be written in exponential form as 21^1/3. The prime factorization of 21 is 3 × 7. It is also an irrational number where ∛21 cannot be expressed in the form of p/q where both p and q are integers and q ≠ 0. 
 

Finding cube roots for perfect cubes is easy, but for non-perfect cubes, the process can be a bit tricky. For non-perfect cubes, we can use Halley’s method. Let’s explore how this method helps us find the cube root of 21.
 

Halley’s method is a step-by-step way to find the cube root of a non-perfect cube number. Here, we will find the value of ‘a’ where a³ is the non-perfect cube

∛a≅  x (x³+2a)/ (2x³+a) is the formula used in this method. 

As 21 is a non-perfect cube number, it lies between the two perfect cube numbers. Here, ‘a’ lies between 8 (2³) and 27 (3³). 

By applying Halley’s Method, we get.

Step 1: Let the number ‘a’ = 21. Start by taking ‘x’ = 2, as 8 (∛8 = 2) is the nearest perfect cube which is closer to 21

Step 2: Apply the value of ‘a=21’ and ‘x=2’ in the formula: 

 ∛a≅  x (x³+2a)/ (2x³+a)

Step 3: The formula will be, 

 ∛21 ≅  2 (2³+2*21) /(2*2³+21)

Step 4: After simplifying, we get the cube root of 21 as 2.7589.

• Fraction: It is a way to show a part of something. For example, in the fraction 2/5 , it means you have 2 out of 5 equal parts. 

• Exponent: It is a smaller number that shows us how many times we multiply the number by itself. For example, in 3³, 3 is the exponent, which means we multiply 3 three times.

• Non-terminating: Numbers that go on infinite times without an end. For example, 3.1415926535