Square Root of 849
2026-02-28 11:26 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-849

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 849, we need to group it as 49 and 8.

Step 2: Now we need to find n whose square is 8 or less. We can say n as '2' because 2 x 2 = 4, which is less than 8. Now the quotient is 2, and after subtracting 4 from 8, the remainder is 4.

Step 3: Now let us bring down 49, making the new dividend 449. Add the old divisor, 2, to itself, getting 4, which will be our new divisor.

Step 4: Find n such that 4n x n is less than or equal to 449. Let's consider n as 9, now 49 x 9 = 441.

Step 5: Subtract 441 from 449, getting a remainder of 8. The quotient is now 29.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to bring two zeroes down to the dividend. Now the new dividend is 800.

Step 7: Now we need to find the new divisor, which is 58, because 581 x 1 = 581.

Step 8: Subtracting 581 from 800 gives us 219.

Step 9: Continue this process until the desired precision is achieved.

So the square root of √849 is approximately 29.14.