Square Root of 3649
2026-02-28 21:43 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3649

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 3649, we need to group it as 49 and 36.

Step 2: Now we need to find n whose square is 36. We can say n as ‘6’ because 6 × 6 = 36. Now the quotient is 6 and the remainder is 0.

Step 3: Now let us bring down 49 which is the new dividend. Add the old divisor with the same number, 6 + 6, we get 12, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 12n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 12n × n ≤ 49. Let us consider n as 4, now 12 × 4 = 48.

Step 6: Subtract 49 from 48, the difference is 1, and the quotient is 60.

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 100.

Step 8: Now we need to find the new divisor, which is 120, because 120 × 0 = 0.

Step 9: Subtracting 0 from 100 we get the result 100.

Step 10: Now the quotient is 60.3.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.

So the square root of √3649 is approximately 60.37.