Last updated on May 26th, 2025
The cube root of a number is a value that when multiplied by itself three times gives back the original number. We apply the function of cube roots in the fields of engineering, designing, financial mathematics, and many more. Let's learn more about the 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 281/3. 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
Making mistakes while learning cube roots is common. Let’s look at some common mistakes kids might make and how to fix them.
What is the cube root of 28 rounded to three decimal places?
The cube root of 28 is approximately 3.037 when rounded to three decimal places.
The cube root of a number is the value that, when multiplied by itself three times, equals the original number. For 28:
∛28 = 3.036588972
When rounded to three decimals, ∛28 3.037
How would you write the cube root of 28 as a mathematical expression?
The cube root of 28 is expressed as 281/3, which is approximately equal to 3.037 when calculated.
The cube root of a number can be written mathematically using the exponent 13. For 28:
∛28 = 281/3
This expression represents the value that, when raised to the power of 3, equals 28. Using a calculator, 281/3 = 3.037 when rounded to three decimal places.
Which two whole numbers does the cube root of 28 fall between?
The cube root of 28 falls between 3 and 4, with an approximate value of 3.037, closer to 3.
The cube root of a number lies between two consecutive whole numbers if the cube of the smaller number is less than the given number, and the cube of the larger number is greater than the given number. For 28:
33= 27 (less than 28)
43= 64 (greater than 28)
Since 28 is closer to 27, its cube root (3.037)is closer to 3.
Is 3.037 the exact cube root of 28?
No, 3.037 is an approximation of the cube root of 28, the exact value is irrational and cannot be represented precisely as a finite decimal.
An irrational number is a number that cannot be expressed as a fraction or as a terminating or repeating decimal. The cube root of 28, written as 328 is an irrational number. When calculated, its decimal representation continues infinitely without repeating, but for practical purposes, it is approximated as 3.037 to three decimal places.
How close is the cube root of 28 to the cube root of 30?
The cube root of 28 is approximately 3.037, while the cube root of 30 is approximately 3.107. The difference between them is approximately 0.07.
The cube root of a number is the value that, when raised to the power of 3, equals the given number. Calculating the cube roots:
∛28 =3.037
∛30 = 3.107
This shows that the cube root of 28 is slightly less than that of 30, with a small difference of approximately 0.07.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.