124 LearnersLast updated on May 26th, 2025
Square Root of 2228
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 2228.
What is the Square Root of 2228?
The square root is the inverse of the square of a number. 2228 is not a perfect square. The square root of 2228 is expressed in both radical and exponential form. In the radical form, it is expressed as √2228, whereas (2228)^(1/2) in exponential form. √2228 ≈ 47.1991, 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 2228
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 2228 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2228 is broken down into its prime factors.
Step 1: Finding the prime factors of 2228 Breaking it down, we get 2 x 2 x 557: 2^2 x 557
Step 2: Now we have found the prime factors of 2228. Since 2228 is not a perfect square, calculating √2228 using prime factorization directly is not feasible.
Square Root of 2228 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 2228, we need to group it as 28 and 22.
Step 2: Now we need to find n whose square is closest to 22. We can say n is 4 because 4^2 = 16, which is lesser than or equal to 22. Now the quotient is 4, and after subtracting 16 from 22, the remainder is 6.
Step 3: Now let us bring down 28 to get the new dividend 628. Add the old divisor with the same number 4 + 4 to get 8, which will be our new divisor.
Step 4: The new divisor will be 8n, and we need to find the value of n such that 8n * n ≤ 628. Let us consider n as 7, now 87 x 7 = 609.
Step 5: Subtract 609 from 628, the difference is 19, and the quotient is 47.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1900.
Step 7: Now we need to find the new divisor that is 944 because 944 x 2 = 1888.
Step 8: Subtracting 1888 from 1900 gives a remainder of 12.
Step 9: Now the quotient is approximately 47.19.
Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √2228 is approximately 47.199.
Square Root of 2228 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 2228 using the approximation method.
Step 1: Now we have to find the closest perfect square of √2228. The smallest perfect square less than 2228 is 2025 (45^2), and the largest perfect square greater than 2228 is 2304 (48^2). Hence, √2228 falls somewhere between 45 and 48.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Going by the formula (2228 - 2025) / (2304 - 2025) ≈ 0.1991
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 + 0.1991 ≈ 47.1991.
So the square root of 2228 is approximately 47.1991.
Common Mistakes and How to Avoid Them in the Square Root of 2228
Students can make mistakes while finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, etc. Now let us look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remind students 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 symbols in proper places
Not using the square root properly is another mistake that students make. It is crucial to teach students to simplify the numbers inside the square root and then move on.
For example, √(12 + 24) = √12 + √24 is incorrect. The correct way is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step for students is to simplify the numbers inside the square root. This is important to avoid mistakes while identifying the approximate value.
For example, √50 ≈ 7.071067, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to understand the difference between cube roots and square roots to 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, which can lead to errors if a step is skipped accidentally, resulting in an incorrect answer. This can happen in subtraction or elsewhere.
Square Root of 2228 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2500?
The area of the square is 2500 square units.
Explanation
The area of the square = side^2.
The side length is given as √2500.
Area of the square = side^2 = √2500 x √2500 = 50 x 50 = 2500.
Therefore, the area of the square box is 2500 square units.
Problem 2
A square-shaped building measures 2228 square feet. If each side is √2228, what will be the square feet of half of the building?
1114 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2228 by 2, we get 1114.
So half of the building measures 1114 square feet.
Problem 3
Calculate √2228 x 5.
235.9955
Explanation
The first step is to find the square root of 2228, which is approximately 47.1991.
The second step is to multiply 47.1991 by 5.
So, 47.1991 x 5 ≈ 235.9955.
Problem 4
What will be the square root of (2220 + 8)?
The square root is approximately 47.1991.
Explanation
To find the square root, calculate the sum of (2220 + 8), which is 2228.
The square root of 2228 is approximately 47.1991.
Therefore, the square root of (2220 + 8) is approximately ±47.1991.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2228 units and the width ‘w’ is 28 units.
The perimeter of the rectangle is approximately 150.3982 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2228 + 28) = 2 × (47.1991 + 28) = 2 × 75.1991 ≈ 150.3982 units.
FAQ on Square Root of 2228
1.What is √2228 in its simplest form?
2.Mention the factors of 2228.
3.Calculate the square of 2228.
4.Is 2228 a prime number?
5.2228 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 2228?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 2228?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 2228
- Square root: A square root is the inverse of a square. For 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 both p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, it is the positive square root that is most often used in real-world applications. This is why it is known as the principal square root.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 28 is 2 x 2 x 7.
- Long division method: A method used to find the square root of non-perfect squares, involving a step-by-step approach of division and subtraction to approximate the square root.
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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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