Square Root of 1249
2026-02-28 23:44 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1249

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. For 1249, we need to group it as 49 and 12.

Step 2: Now we need to 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. Subtracting 9 from 12, the remainder is 3.

Step 3: Bring down 49, making the new dividend 349. Add the old divisor with the same number 3 + 3 = 6, which will be our new divisor.

Step 4: The new divisor, 6n, needs to be multiplied by n to get a product less than or equal to 349. Let us consider n as 5, now 65 x 5 = 325.

Step 5: Subtract 325 from 349, the difference is 24, and the quotient is 35.

Step 6: 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 2400.

Step 7: The next new divisor is 70, and we need to find n such that 700n x n ≤ 2400. Let n be 3, then 703 x 3 = 2109.

Step 8: Subtracting 2109 from 2400 gives a remainder of 291.

Step 9: The current quotient is 35.3. Continue these steps until we get two numbers after the decimal point.

So the square root of √1249 is approximately 35.33.