Square Root of 277
2026-02-28 01:33 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-277

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 277, we need to group it as 77 and 2.

Step 2: Now we need to find a number whose square is less than or equal to 2. The closest number is 1 because 1 × 1 = 1. Now the quotient is 1, and after subtracting 1 from 2, the remainder is 1.

Step 3: Now let us bring down 77 to make it 177. Add the old divisor with the same number (1 + 1 = 2), which will be our new divisor.

Step 4: The new divisor will be 2n. We need to find the value of n such that 2n × n ≤ 177. Let us consider n as 6, now 26 × 6 = 156.

Step 5: Subtract 156 from 177, the difference is 21, and the quotient is 16.

Step 6: 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 2100.

Step 7: Now we need to find the new divisor that is 9 because 329 × 9 = 2961

Step 8: Subtracting 2961 from 2100 results in a negative number. So, adjust the divisor to 328 × 6 = 1968.

Step 9: Subtracting 1968 from 2100, we get the result 132.

Step 10: Now the quotient is 16.6

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 √277 ≈ 16.64