Square Root of 1775
2026-02-28 13:32 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1775

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 1775, we need to group it as 75 and 17.

Step 2: Now we need to find n whose square is 16. We can say n as ‘4’ because 4 x 4 is lesser than or equal to 17. Now the quotient is 4, after subtracting 16 from 17, the remainder is 1.

Step 3: Now, let us bring down 75, which is the new dividend. Add the old divisor with the same number 4 + 4, we get 8, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 8n × n ≤ 175. Let us consider n as 2, now 82 x 2 = 164.

Step 6: Subtract 175 from 164, the difference is 11, and the quotient is 42.

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 1100.

Step 8: Now, we need to find the new divisor. That is 421 because 421 x 2 = 842.

Step 9: Subtracting 842 from 1100, we get the result 258.

Step 10: Now the quotient is 42.1.

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

So the square root of √1775 is approximately 42.13.