Square Root of 775
2026-02-28 13:16 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-775

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 775, we need to group it as 75 and 7.

Step 2: Now we need to find n whose square is 7. We can say n as ‘2’ because 2 x 2 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 75, 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 4n. We need to find the value of n.

Step 5: The next step is finding 4n x n ≤ 375. Let us consider n as 7, now 47 x 7 = 329.

Step 6: Subtract 329 from 375, the difference is 46, 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 zeroes to the dividend. Now the new dividend is 4600.

Step 8: Now we need to find the new divisor that is 554 because 554 x 8 = 4432.

Step 9: Subtracting 4432 from 4600, we get the result 168.

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 are no decimal values, continue till the remainder is zero.

So the square root of √775 is approximately 27.84.