Square Root of 1377
2026-02-28 10:19 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1377

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 1377, we need to group it as 77 and 13.

Step 2: Now we need to find n whose square is 13. We can say n as ‘3’ because 3 x 3 is lesser than or equal to 13. Now the quotient is 3, after subtracting 13 - 9 the remainder is 4.

Step 3: Now let us bring down 77 which is the new dividend. Add the old divisor with the same number 3 + 3 we get 6 which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 6n x n ≤ 477. Let us consider n as 7, now 6 x 7 x 7 = 294.

Step 6: Subtract 477 from 294, the difference is 183, and the quotient is 37.

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 18300.

Step 8: Now we need to find the new divisor that is 741 because 741 x 1 = 741.

Step 9: Subtracting 741 from 18300, we get the result 17559.

Step 10: Now the quotient is 37.1.

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 √1377 is approximately 37.10.