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Last updated on May 26th, 2025

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Square Root of 2209

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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.

Square Root of 2209 for Indian Students
Professor Greenline from BrightChamps

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.

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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
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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.

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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.

Professor Greenline from BrightChamps

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.

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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

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Forgetting about the Negative Square Root

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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.

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Square Root of 2209 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the perimeter of a square box if its side length is √2209?

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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.

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Max, the Girl Character from BrightChamps

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?

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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.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √2209 x 5.

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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.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (2200 + 9)?

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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.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √2209 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is 170 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (47 + 38) = 2 × 85 = 170 units.

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FAQ on Square Root of 2209

1.What is √2209 in its simplest form?

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2.Mention the factors of 2209.

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3.Calculate the square of 2209.

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4.Is 2209 a prime number?

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5.2209 is divisible by?

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6.How does learning Algebra help students in India make better decisions in daily life?

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7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 2209?

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8.How do technology and digital tools in India support learning Algebra and Square Root of 2209?

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9.Does learning Algebra support future career opportunities for students in India?

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Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

About BrightChamps in India

At BrightChamps, we see algebra as more than just symbols—it opens doors to endless opportunities! Our mission is to help children all over India develop vital math skills, focusing today on the Square Root of 2209 with special attention to understanding square roots—in a way that’s engaging, lively, and easy to follow. Whether your child is calculating the speed of a passing train, keeping scores during a cricket match, or managing pocket money for the latest gadgets, mastering algebra gives them the confidence needed for everyday situations. Our interactive lessons keep learning simple and fun. As kids in India have varied learning styles, we personalize our approach to match each child. From the busy markets of Mumbai to Delhi’s vibrant streets, BrightChamps brings math to life, making it relatable and exciting throughout India. Let’s make square roots a joyful part of every child’s math journey!
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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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Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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