103 LearnersLast updated on May 26th, 2025
Square Root of 2809
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 2809.
What is the Square Root of 2809?
The square root is the inverse of the square of the number. 2809 is a perfect square. The square root of 2809 is expressed in both radical and exponential form. In the radical form, it is expressed as √2809, whereas 2809^(1/2) in the exponential form. √2809 = 53, 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 2809
The prime factorization method is used for perfect square numbers. Let us now learn the following methods:
- Prime factorization method
- Long division method
Square Root of 2809 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2809 is broken down into its prime factors.
Step 1: Finding the prime factors of 2809 Breaking it down, we get 53 x 53: 53^2
Step 2: Now we found out the prime factors of 2809. Since 2809 is a perfect square, we can group the prime factors in pairs.
Therefore, the square root of 2809 using prime factorization is 53.
Square Root of 2809 by Long Division Method
The long division method is particularly used for non-perfect square numbers as well, but it can be applied to perfect squares for verification. 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: Start by pairing the digits from right to left. In the case of 2809, we pair it as 28 and 09.
Step 2: Find the largest number whose square is less than or equal to the first pair (28). That number is 5 because 5 x 5 = 25, and 25 is less than 28.
Step 3: Subtract 25 from 28, leaving a remainder of 3. Bring down the next pair of digits (09) to make it 309.
Step 4: Double the divisor (5), which gives 10.
Step 5: Find a digit (n) such that 10n x n is less than or equal to 309. That digit is 3, because 103 x 3 = 309.
Step 6: Subtract 309 from 309, leaving a remainder of 0.
Step 7: The quotient 53 is the square root of 2809.
Square Root of 2809 by Approximation Method
The approximation method is not necessary for perfect squares like 2809, as it gives an exact integer value. However, this method can be useful for non-perfect squares.
Common Mistakes and How to Avoid Them in the Square Root of 2809
Students do make mistakes while finding the square root, such as 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, √2809 = 53, there is also -53 which should not be forgotten.
Square Root of 2809 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2809?
The area of the square is 2809 square units.
Explanation
The area of the square = side².
The side length is given as √2809.
Area of the square = side²
= √2809 x √2809
= 53 × 53
= 2809.
Therefore, the area of the square box is 2809 square units.
Problem 2
A square-shaped building measuring 2809 square feet is built; if each of the sides is √2809, what will be the square feet of half of the building?
1404.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2809 by 2 = we get 1404.5.
So half of the building measures 1404.5 square feet.
Problem 3
Calculate √2809 x 5.
265
Explanation
The first step is to find the square root of 2809, which is 53.
The second step is to multiply 53 by 5.
So 53 x 5 = 265.
Problem 4
What will be the square root of (2500 + 309)?
The square root is 53.
Explanation
To find the square root, we need to find the sum of (2500 + 309).
2500 + 309 = 2809, and then √2809 = 53.
Therefore, the square root of (2500 + 309) is ±53.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2809 units and the width ‘w’ is 10 units.
We find the perimeter of the rectangle as 126 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2809 + 10)
= 2 × (53 + 10)
= 2 × 63
= 126 units.
FAQ on Square Root of 2809
1.What is √2809 in its simplest form?
2.Is 2809 a perfect square?
3.Calculate the square of 2809.
4.Is 2809 a prime number?
5.2809 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 2809?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 2809?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 2809
- Square root: A square root is the inverse of a square. Example: 5² = 25, and the inverse of the square is the square root, that is, √25 = 5.
- 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. For example, 9 is a perfect square because it is 3².
- Integer: An integer is a whole number that can be positive, negative, or zero, such as -5, 0, 4, etc.
- Long division method: A method used to find the square root of a number by dividing and averaging to get a more precise result.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
