Square Root of 789
2026-02-28 12:22 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-789

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 789, we need to group it as 89 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: Now let us bring down 89, which is the new dividend. Add the old divisor with the same number 2 + 2 = 4, which will be our new divisor.

Step 4: The new divisor will be 4n, and we need to find the value of n such that 4n × n ≤ 389. Let n be 7, now 47 × 7 = 329.

Step 5: Subtract 329 from 389. The difference is 60, and the quotient is 27.

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 zeros to the dividend. Now the new dividend is 6000.

Step 7: Now we need to find the new divisor that is 547 because 547 × 9 = 4923.

Step 8: Subtracting 4923 from 6000 gives the result 1077.

Step 9: 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 √789 is approximately 28.08.