118 LearnersLast updated on May 26th, 2025
Square Root of 2028
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 2028.
What is the Square Root of 2028?
The square root is the inverse of the square of the number. 2028 is not a perfect square. The square root of 2028 is expressed in both radical and exponential form. In the radical form, it is expressed as √2028, whereas (2028)^(1/2) in the exponential form. √2028 ≈ 45.025, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 2028
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2028 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2028 is broken down into its prime factors:
Step 1: Finding the prime factors of 2028
Breaking it down, we get 2 × 2 × 3 × 13 × 13: 2^2 × 3^1 × 13^2
Step 2: Now we found out the prime factors of 2028. The second step is to make pairs of those prime factors. Since 2028 is not a perfect square, the digits of the number can’t be grouped in a perfect pair. Therefore, calculating 2028 using prime factorization is possible but results in an irrational number.
Square Root of 2028 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 2028, we need to group it as 28 and 20.
Step 2: Now we need to find n whose square is 20. We can say n as '4' because 4 × 4 = 16, which is less than 20. Now the quotient is 4, and after subtracting 16 from 20, the remainder is 4.
Step 3: Now let us bring down 28, making it 428 as the new dividend. Add 4 to the old divisor to get 8, which will be our new divisor.
Step 4: Find a digit n such that 8n × n ≤ 428. Let us consider n as 5, now 85 × 5 = 425.
Step 5: Subtract 425 from 428, the difference is 3, and the quotient becomes 45.
Step 6: Since the remainder is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 300.
Step 7: The new divisor is 90 because 901 × 1 = 90.
Step 8: Subtracting 90 from 300, we get the result 210.
Step 9: Now the quotient is 45.0. Continue these steps until we get two numbers after the decimal point or until the remainder is zero.
So the square root of √2028 ≈ 45.025.
Square Root of 2028 by Approximation Method
The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 2028 using the approximation method.
Step 1: Find the closest perfect square of √2028. The smallest perfect square less than 2028 is 2025 (which is 45^2), and the next perfect square is 2116 (which is 46^2). √2028 falls somewhere between 45 and 46.
Step 2: Now we apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Going by the formula (2028 - 2025) ÷ (2116 - 2025) = 3 ÷ 91 ≈ 0.033.
Using the formula we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 45 + 0.033 = 45.033, so the square root of 2028 is approximately 45.033.
Common Mistakes and How to Avoid Them in the Square Root of 2028
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √50 = 7.07, there is also -7.07 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12+24) = √12 + √24 is a wrong method of using roots. The right way of using roots is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 = 7 is wrong, the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them avoid mistakes.
For example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the Long Division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the calculation. This may either happen in subtracting or elsewhere.
Square root of 2028 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2028?
The area of the square is 2028 square units.
Explanation
The area of the square = side^2.
The side length is given as √2028.
Area of the square = side^2 = √2028 × √2028 = 2028.
Therefore, the area of the square box is 2028 square units.
Problem 2
A square-shaped building measuring 2028 square feet is built; if each of the sides is √2028, what will be the square feet of half of the building?
1014 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2028 by 2 = we get 1014.
So half of the building measures 1014 square feet.
Problem 3
Calculate √2028 × 5.
225.125
Explanation
The first step is to find the square root of 2028, which is approximately 45.025.
The second step is to multiply 45.025 by 5.
So 45.025 × 5 ≈ 225.125.
Problem 4
What will be the square root of (2028 + 4)?
The square root is approximately 45.177.
Explanation
To find the square root, we need to find the sum of (2028 + 4). 2028 + 4 = 2032, and then √2032 ≈ 45.177.
Therefore, the square root of (2028 + 4) is approximately ±45.177.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2028 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 166.05 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2028 + 38) = 2 × (45.025 + 38) = 2 × 83.025 ≈ 166.05 units.
FAQ on Square Root of 2028
1.What is √2028 in its simplest form?
2.Mention the factors of 2028.
3.Calculate the square of 2028.
4.Is 2028 a prime number?
5.2028 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 2028?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 2028?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 2028
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
- Perfect square: A perfect square is a number that can be expressed as the product of an integer with itself. For example, 9 is a perfect square because it can be written as 3 × 3.
- Long division method: A technique used to find the square root of a number, especially when the number is not a perfect square, involving iterative steps of division and subtraction.
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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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