129 LearnersLast updated on May 26th, 2025
Square Root of 2209
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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 2209.
What is the Square Root of 2209?
The square root is the inverse of the square of a number. 2209 is a perfect square. The square root of 2209 is expressed in both radical and exponential form. In the radical form, it is expressed as √2209, whereas (2209)^(1/2) in the exponential form. √2209 = 47, which is a rational number because it can be expressed in the form of p/q, where p and q are integers, and q ≠ 0.
Finding the Square Root of 2209
The prime factorization method is used for perfect square numbers. Since 2209 is a perfect square, we will use the prime factorization method. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2209 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2209 is broken down into its prime factors:
Step 1: Finding the prime factors of 2209 Breaking it down, we get 47 x 47.
Step 2: Now we found out the prime factors of 2209. Since 2209 is a perfect square, therefore, the digits of the number can be grouped in pairs.
Square Root of 2209 by Long Division Method
The long division method is particularly used for both perfect and 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 2209, we need to group it as 09 and 22.
Step 2: Now we need to find a number whose square is less than or equal to 22. We can say 4 because 4 x 4 = 16 which is less than 22. Now the quotient is 4, after subtracting 16 from 22, the remainder is 6.
Step 3: Now bring down 09 to make it 609 as the new dividend. 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 ≤ 609. Let us consider n as 7, now 87 x 7 = 609.
Step 6: Subtract 609 from 609, the difference is 0, and the quotient is 47. Since the remainder is zero, we have found the exact square root of 2209, which is 47.
Square Root of 2209 by Approximation Method
Since 2209 is a perfect square, an approximation is not necessary. However, if it were not, the approximation method could be used to find an approximate value.
Common Mistakes and How to Avoid Them in the Square Root of 2209
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. 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 has both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √2209 = 47, there is also -47 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 before moving on to the second step.
For example: √(16 + 9) = √16 + √9 is wrong. The correct method is √(16 + 9) = √25 = 5.
Mistake 3
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: √64 and ∛64 are different.
Mistake 4
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 sum.
Square Root of 2209 Examples
Problem 1
Can you help Max find the perimeter of a square box if its side length is √2209?
The perimeter of the square is 188 units.
Explanation
The perimeter of the square = 4 × side.
The side length is given as √2209 = 47. Perimeter = 4 × 47 = 188.
Therefore, the perimeter of the square box is 188 units.
Problem 2
A square-shaped building measuring 2209 square feet is built; if each of the sides is √2209, what will be the square feet of half of the building?
1104.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2209 by 2 = 1104.5.
So half of the building measures 1104.5 square feet.
Problem 3
Calculate √2209 x 5.
235
Explanation
The first step is to find the square root of 2209, which is 47.
The second step is to multiply 47 by 5.
So 47 x 5 = 235.
Problem 4
What will be the square root of (2200 + 9)?
The square root is 47.
Explanation
To find the square root, we need to find the sum of (2200 + 9) = 2209, and then √2209 = 47.
Therefore, the square root of (2200 + 9) is ±47.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √2209 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 170 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (47 + 38) = 2 × 85 = 170 units.
FAQ on Square Root of 2209
1.What is √2209 in its simplest form?
2.Mention the factors of 2209.
3.Calculate the square of 2209.
4.Is 2209 a prime number?
5.2209 is divisible by?
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 Square Root of 2209?
8.How do technology and digital tools in India support learning Algebra and Square Root of 2209?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 2209
- Square root: A square root is the inverse of a square. Example: 7² = 49 and the inverse of the square is the square root, that is, √49 = 7.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 9 is a perfect square because it is 3².
- Prime factorization: Prime factorization is the process of writing a number as a product of its prime numbers.
- Divisor: A divisor is a number by which another number is to be divided.
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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.
Fun Fact
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