Square Root of 769
2026-02-28 23:37 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-769

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 769, we need to group it as 69 and 7.

Step 2: Now we need to find n whose square is less than or equal to 7. We can say n is ‘2’ because 2 × 2 = 4, which is less than 7. Now the quotient is 2, and after subtracting 4 from 7, the remainder is 3.

Step 3: Bring down 69 to make it 369. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.

Step 4: Use 4 as the new divisor. Now we get 4n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 4n × n ≤ 369. Let us consider n as 7. Now, 47 × 7 = 329.

Step 6: Subtract 329 from 369 to get the difference of 40, and the quotient is 27.

Step 7: Since the remainder 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 4000.

Step 8: Find the new divisor, which would be 54 because 547 × 7 = 3829.

Step 9: Subtracting 3829 from 4000 gives us the result 171.

Step 10: Now the quotient is 27.7.

Step 11: Continue doing these steps until we get the desired precision. Suppose if there is no more remainder, continue till the remainder is zero.

So the square root of √769 is approximately 27.73.