Square Root of 773
2026-02-28 21:46 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-773

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 773, we need to group it as 73 and 7.

Step 2: Now we need to find n whose square is less than or equal to 7. We can say n as ‘2’ because 2 x 2 is 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 73, which is the new dividend. Add the old divisor's double to itself, 2 x 2 = 4, which will be our new divisor.

Step 4: The new divisor becomes 4n. We need to find the value of n.

Step 5: The next step is finding 4n × n ≤ 373. Let us consider n as 7, now 47 x 7 = 329.

Step 6: Subtract 329 from 373; the difference is 44, and the quotient is 27.

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 zeros to the dividend. Now the new dividend is 4400.

Step 8: Now we need to find the new divisor, which is 8 because 548 x 8 = 4384.

Step 9: Subtracting 4384 from 4400, we get the result 16.

Step 10: Now the quotient is 27.8.

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 √773 ≈ 27.8.