Last updated on May 26th, 2025
If a number is multiplied by itself, 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 1244.
The square root is the inverse of the square of a number. 1244 is not a perfect square. The square root of 1244 is expressed in both radical and exponential form. In the radical form, it is expressed as √1244, whereas in exponential form it is (1244)^(1/2). √1244 ≈ 35.257, which is an irrational number because it cannot be expressed in the form p/q, where p and q are integers and q ≠ 0.
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and approximation method are used. 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 1244 is broken down into its prime factors:
Step 1: Finding the prime factors of 1244. Breaking it down, we get 2 x 2 x 311: 2^2 x 311.
Step 2: Now we found out the prime factors of 1244. The second step is to make pairs of those prime factors. Since 1244 is not a perfect square, the digits of the number can’t be grouped in pairs.
Thus, calculating 1244 using prime factorization is not straightforward.
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, group the numbers from right to left. In the case of 1244, group it as 12 and 44.
Step 2: Now find n whose square is less than or equal to 12. We can say n is 3 because 3 x 3 = 9, which is less than 12. Now the quotient is 3, and after subtracting, 12 - 9, the remainder is 3.
Step 3: Bring down 44, which is the new dividend. Add the old divisor's last digit (3) to the same number to get 6, which will be our new divisor.
Step 4: The new divisor is 6n. Find the value of n such that 6n x n ≤ 344.
Step 5: Let n be 5, now 65 x 5 = 325.
Step 6: Subtract 344 from 325; the difference is 19, and the quotient is 35.
Step 7: Since the dividend is less than the divisor, add a decimal point, allowing us to bring down two zeroes to the dividend. Now the new dividend is 1900.
Step 8: Find the new divisor, which is 702, since 702 x 2 = 1404.
Step 9: Subtracting 1404 from 1900 gives a result of 496.
Step 10: Now the quotient is 35.2.
Step 11: Continue these steps until we get the desired decimal places.
So the square root of √1244 is approximately 35.257.
The approximation method is another method for finding square roots; it is an easy way to find the square root of a given number. Now let us learn how to find the square root of 1244 using the approximation method.
Step 1: Find the closest perfect square to √1244. The smallest perfect square less than 1244 is 1225, and the largest perfect square greater than 1244 is 1296. √1244 lies between 35 and 36.
Step 2: Apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula, (1244 - 1225) ÷ (1296 - 1225) = 19 ÷ 71 ≈ 0.2676. Adding this value to the smaller perfect square root, we get 35 + 0.2676 ≈ 35.2676.
Thus, the square root of 1244 is approximately 35.2676.
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √1244?
The area of the square is approximately 1549.536 square units.
The area of a square = side².
The side length is given as √1244.
Area of the square = (√1244)² = 1244 square units.
A square-shaped building measuring 1244 square feet is built; if each of the sides is √1244, what will be the square feet of half of the building?
622 square feet
Divide the given area by 2 as the building is square-shaped.
Dividing 1244 by 2, we get 622.
So, half of the building measures 622 square feet.
Calculate √1244 x 5.
Approximately 176.285
First, find the square root of 1244, which is approximately 35.257.
Then multiply 35.257 by 5.
So, 35.257 x 5 ≈ 176.285.
What will be the square root of (1244 + 32)?
The square root is 36.
To find the square root, first find the sum of (1244 + 32).
1244 + 32 = 1276, and then find √1276, which is approximately 35.7.
Therefore, the square root of (1244 + 32) is about ±35.7.
Find the perimeter of the rectangle if its length ‘l’ is √1244 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 170.514 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1244 + 50)
≈ 2 × (35.257 + 50)
≈ 2 × 85.257
≈ 170.514 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.
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