115 LearnersLast updated on May 26th, 2025
Square Root of 2260
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 2260.
What is the Square Root of 2260?
The square root is the inverse of the square of a number. 2260 is not a perfect square. The square root of 2260 is expressed in both radical and exponential form. In the radical form, it is expressed as √2260, whereas (2260)^(1/2) in the exponential form. √2260 ≈ 47.549, 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 2260
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 2260 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2260 is broken down into its prime factors.
Step 1: Finding the prime factors of 2260 Breaking it down, we get 2 x 2 x 5 x 113: 2^2 x 5^1 x 113^1
Step 2: Now we found the prime factors of 2260. The second step is to make pairs of those prime factors. Since 2260 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating √2260 using prime factorization directly is not feasible.
Square Root of 2260 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 2260, we need to group it as 60 and 22.
Step 2: Now, we need to find n whose square is 22. We can say n as ‘4’ because 4 x 4 = 16, which is less than 22. Now the quotient is 4, and after subtracting 16 from 22, the remainder is 6.
Step 3: Now let us bring down 60, making the new dividend 660. 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 the sum of the dividend and quotient. Now we get 8n as the new divisor; we need to find the value of n.
Step 5: The next step is finding 8n x n ≤ 660. Let's consider n as 7, so 87 x 7 = 609.
Step 6: Subtract 609 from 660; the difference is 51, and the quotient is 47.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal allows us to add two zeros to the dividend. Now the new dividend is 5100.
Step 8: Now we need to find the new divisor, 945, because 945 x 5 = 4725.
Step 9: Subtracting 4725 from 5100 gives us 375.
Step 10: Now the quotient is 47.5.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.
So the square root of √2260 ≈ 47.55.
Square Root of 2260 by Approximation Method
The approximation method is another method for finding the 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 2260 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √2260. The smallest perfect square smaller than 2260 is 2025, and the largest perfect square larger than 2260 is 2304. √2260 falls somewhere between 45 and 48.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula (2260 - 2025) ÷ (2304 - 2025) = 0.836.
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 + 0.836 = 45.836.
So the square root of 2260 is approximately 45.836.
Common Mistakes and How to Avoid Them in the Square Root of 2260
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make 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: √225 = 15, and there is also -15, which should not be forgotten.
Mistake 2
Not adding the 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: √(25 + 9) = √25 + √9 is the wrong method. The right way is √(25 + 9) = √34.
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 keep away from 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, resulting in a wrong answer at the end. This may either happen in subtracting or elsewhere.
Square Root of 2260 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2260?
The area of the square is approximately 2260 square units.
Explanation
The area of the square = side^2.
The side length is given as √2260.
Area of the square = side^2 = √2260 x √2260 = 2260.
Therefore, the area of the square box is approximately 2260 square units.
Problem 2
A square-shaped building measuring 2260 square feet is built; if each of the sides is √2260, what will be the square feet of half of the building?
1130 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2260 by 2 = 1130.
So half of the building measures 1130 square feet.
Problem 3
Calculate √2260 x 5.
Approximately 237.745
Explanation
The first step is to find the square root of 2260, which is approximately 47.549.
The second step is to multiply 47.549 by 5.
So 47.549 x 5 ≈ 237.745.
Problem 4
What will be the square root of (2025 + 235)?
The square root is approximately 48.
Explanation
To find the square root, we need to find the sum of (2025 + 235).
2025 + 235 = 2260.
The square root of 2260 is approximately 48.
Therefore, the square root of (2025 + 235) is approximately ±48.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2260 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 195.098 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2260 + 50) ≈ 2 × (47.549 + 50) ≈ 2 × 97.549 ≈ 195.098 units.
FAQ on Square Root of 2260
1.What is √2260 in its simplest form?
2.Mention the factors of 2260.
3.Calculate the square of 2260.
4.Is 2260 a prime number?
5.2260 is divisible by?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 2260?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 2260?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 2260
- 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 is often used in practical applications, known as the principal square root.
- Prime factorization: The process of breaking down a composite number into its prime factors. For example, the prime factorization of 18 is 2 x 3^2.
- Long division method: A step-by-step method used to find the square root of numbers, especially non-perfect squares, through division.
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Jaskaran Singh Saluja
About the Author
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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