Square Root of 627
2026-02-28 00:52 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-627

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 627, we need to group it as 27 and 6.

Step 2: Now we need to find n whose square is 6. We can say n is ‘2’ because 2 x 2 = 4, which is lesser than or equal to 6. Now the quotient is 2, and after subtracting 4 from 6, the remainder is 2.

Step 3: Now let us bring down 27, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

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

Step 5: The next step is finding 4n x n ≤ 227. Let us consider n as 5, now 45 x 5 = 225.

Step 6: Subtract 225 from 227, and the difference is 2.

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 200.

Step 8: Now we need to find the new divisor. 5 is our next digit because 405 x 5 = 2025.

Step 9: Subtracting 2025 from 2000, we get the result -25, indicating we should adjust our last digit to a lower number and continue the process until the remainder is zero or until an acceptable decimal precision is achieved.

Step 10: 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 √627 is approximately 25.06.