123 LearnersLast updated on May 26th, 2025
Square Root of 2409
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 various fields such as engineering, finance, and architecture. Here, we will discuss the square root of 2409.
What is the Square Root of 2409?
The square root is the inverse of squaring a number. 2409 is not a perfect square. The square root of 2409 is expressed in both radical and exponential form. In radical form, it is expressed as √2409, whereas (2409)^(1/2) in exponential form. √2409 ≈ 49.085, 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 2409
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and the approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2409 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2409 is broken down into its prime factors.
Step 1: Finding the prime factors of 2409 Breaking it down, we get 3 x 3 x 7 x 7 x 17: 3² x 7² x 17
Step 2: Now we found out the prime factors of 2409. Since 2409 is not a perfect square, therefore, calculating √2409 using prime factorization is not straightforward.
Square Root of 2409 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 2409, we need to group it as 24 and 09.
Step 2: Now we need to find n whose square is less than or equal to 24. We can say n is ‘4’ because 4 x 4 = 16, which is less than or equal to 24. Subtracting, we get 24 - 16 = 8.
Step 3: Now let us bring down 09 which is the new dividend. Add the old divisor with the same number 4 + 4 = 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 × n ≤ 809. Let us consider n as 9, now 89 x 9 = 801.
Step 6: Subtract 809 from 801; the difference is 8, and the quotient is 49.
Step 7: 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 800.
Step 8: Now we need to find the new divisor that is 981 because 981 × 8 = 7848.
Step 9: Subtracting 7848 from 8000, we get the result 152.
Step 10: Now the quotient is 49.08.
Step 11: 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 √2409 is approximately 49.08.
Square Root of 2409 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 2409 using the approximation method.
Step 1: Now we have to find the closest perfect square of √2409. The smallest perfect square less than 2409 is 2304, and the largest perfect square greater than 2409 is 2500. √2409 falls somewhere between 48 and 50.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Going by the formula (2409 - 2304) ÷ (2500 - 2304) = 0.525
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 48 + 0.525 = 48.525, so the square root of 2409 is approximately 49.085.
Common Mistakes and How to Avoid Them in the Square Root of 2409
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, 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 has both positive and negative square roots. However, we typically use the positive square root, as it is the required one for practical applications.
For example: √50 = 7.07, but there is also -7.07, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol 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, √(12+24) = √36 is correct, not √12 + √24.
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 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube roots and square roots constantly, as this will help them 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. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end. This may either happen in subtracting or elsewhere.
Square Root of 2409 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2409?
The area of the square is approximately 2409 square units.
Explanation
The area of the square = side².
The side length is given as √2409.
Area of the square = side² = √2409 x √2409 = 2409
Therefore, the area of the square box is approximately 2409 square units.
Problem 2
A square-shaped garden measuring 2409 square feet is built; if each of the sides is √2409, what will be the square feet of half of the garden?
1204.5 square feet
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 2409 by 2 = we get 1204.5
So half of the garden measures 1204.5 square feet.
Problem 3
Calculate √2409 x 5.
Approximately 245.425
Explanation
The first step is to find the square root of 2409, which is approximately 49.085.
The second step is to multiply 49.085 by 5.
So 49.085 x 5 ≈ 245.425
Problem 4
What will be the square root of (2209 + 200)?
The square root is approximately 49.497.
Explanation
To find the square root, we need to find the sum of (2209 + 200).
2209 + 200 = 2409, and then √2409 ≈ 49.085.
Therefore, the square root of (2209 + 200) is approximately ±49.085.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2409 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 198.17 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2409 + 50) ≈ 2 × (49.085 + 50) ≈ 2 × 99.085 ≈ 198.17 units.
FAQ on Square Root of 2409
1.What is √2409 in its simplest form?
2.Mention the factors of 2409.
3.Calculate the square of 2409.
4.Is 2409 a prime number?
5.2409 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 2409?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 2409?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 2409
- Square root: The square root of a number is the value that, when multiplied by itself, gives the original number. For example, √16 = 4.
- Irrational number: An irrational number is a number that cannot be written as a simple fraction; it has a non-repeating, non-terminating decimal expansion.
- Radical: A radical is a symbol (√) that represents the root of a number.
- Perfect square: A perfect square is a number that is the square of an integer, such as 1, 4, 9, 16, etc.
- Exponential form: In mathematics, exponential form expresses a number using a base and an exponent, such as (2409)^(1/2) for the square root of 2409.
Explore More algebra
About BrightChamps in United Arab Emirates
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.
