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:

• Prime factorization method
• Long division method
• Approximation method

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.

• Square root: A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse is √16 = 4.
   
• Irrational number: An irrational number is a number that cannot be exactly expressed as a simple fraction.
   
• Principal square root: The non-negative square root of a number, which is usually the more commonly used in practical applications.
   
• Prime factorization: Expressing a number as the product of its prime factors.
   
• Approximation: A method of finding a value that is close enough to the right answer, usually within an acceptable error margin.