210 LearnersLast updated on May 26th, 2025
Cube Root of 28
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.
What is 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 the Cube Root of 28
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.
Cube Root of 28 by Halley’s Method
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
Common Mistakes and How to Avoid Them in the Cube Root of 28
Making mistakes while learning cube roots is common. Let’s look at some common mistakes kids might make and how to fix them.
Mistake 1
Incorrect calculation after applying values in the formula
Sometimes instead of using the ‘+’ symbol, kids may accidentally use the multiplication symbol ‘×’. This can lead to wrong calculations and incorrect results. Always double-check the symbols used in the formula to make sure you’re adding, not multiplying, when needed.
Cube Root of 28 Examples
Problem 1
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.
Explanation
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
Problem 2
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.
Explanation
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.
Problem 3
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.
Explanation
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.
Problem 4
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.
Explanation
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.
Problem 5
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.
Explanation
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.
FAQs For Cube Root Of 28
1.Is the cube root of 28 rational?
2.What is the cube root of 28?
3.How do you manually calculate the cube root of 28?
4.What are some methods to approximate the cube root of 28?
5.What is the cube root of 28 to more decimal places?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Cube Root of 28?
8.How do technology and digital tools in India support learning Algebra and Cube Root of 28?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries For Cube Root Of 28
- 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.
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Jaskaran Singh Saluja
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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.
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