Cube Root of 28

The cube root can be classified into two categories: perfect cubes and non-perfect cubes. For example, the cube root of 64 is 4 which is a whole number, making it a perfect cube. However, the cube root of 28 is not a whole number. The cube root of 28 is approximately 3.04.

The cube root of 28 is represented using the radical sign as ∛28, and can also be written in exponential form as 28^1/3. The prime factorization of 28 is 2² × 7. It is also an irrational number where ∛28 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 28.
 

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 28 is a non-perfect cube number, it lies between the two perfect cube numbers. Here, ‘a’ lies between 27 (3³) and 64 (4³). 

By applying Halley’s Method, we get.

Step 1: Let the number ‘a’ = 28. Start by taking ‘x’ = 3, as 27 (∛27 = 3) is the nearest perfect cube which is closer to 28

Step 2: Apply the value of ‘a = 28’ and ‘x = 3’ in the formula: 

 ∛a≅  x (x³+2a) / (2x³+a)

Step 3: The formula will be, 

 ∛28 ≅  3 x (3³+2*28) / (2*3³+28)

Step 4: After simplifying, we get the cube root of 28 as 3.036588972
 

• Fraction: It is a way to show a part of something. For example, in the fraction 25 , 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

• Decimal: A number that includes a whole part and a fractional part, which is separated by a dot (.) like 0.5, 3.14, etc., 

• Perfect cube: A number that can be expressed as the product of a whole number multiplied by itself three times, like the cube root of 8 is 2 which is a perfect cube. However, the number cannot be expressed as a whole number when finding its cube root, a non-perfect cube like 28.