Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √2209 x 5.
235
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.
What will be the square root of (2200 + 9)?
The square root is 47.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (47 + 38) = 2 × 85 = 170 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.