Square Root of 806
2026-02-28 23:33 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-806

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 806, we need to group it as 06 and 8.

Step 2: Now we need to find n whose square is closest to 8. We can say n as ‘2’ because 2 x 2 = 4 is lesser than or equal to 8. Now the quotient is 2, after subtracting 8 - 4, the remainder is 4.

Step 3: Now let us bring down 06, which is the new dividend. Add the old divisor with the same number 2 + 2; we get 4, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. 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 x n ≤ 406. Let us consider n as 7, now 47 x 7 = 329.

Step 6: Subtract 406 from 329; the difference is 77, and the quotient is 27.

Step 7: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 7700.

Step 8: Now we need to find the new divisor, which is 549 because 549 x 9 = 4941.

Step 9: Subtracting 4941 from 7700, we get the result 2759.

Step 10: Now the quotient is 28.4

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

So the square root of √806 is approximately 28.4.