Square Root of 786
2026-02-28 01:18 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-786

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 786, we need to group it as 86 and 7.

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

Step 3: Now let us bring down 86, which is the new dividend. Add the old divisor with the same number, 2 + 2, to get 4, which will be our new divisor.

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

Step 5: The next step is finding 4n × n ≤ 386. Let us consider n as 9, now 49 × 9 = 441. Since 441 is greater than 386, try n = 8. 48 × 8 = 384.

Step 6: Subtract 384 from 386; the difference is 2, and the quotient is 28.

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 200.

Step 8: Now we need to find the new divisor that is 561 because 5611 × 1 = 561.

Step 9: Subtract 561 from 2000; we get the result 1439.

Step 10: Now the quotient is 28.0.

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

So the square root of √786 ≈ 28.03.