Square Root of 634
2026-02-28 10:21 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-634

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 634, we group it as 34 and 6.

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

Step 3: Bring down 34 to make the new dividend 234.

Step 4: Add the previous divisor with the same number, 2 + 2 = 4, which will be our new divisor.

Step 5: Find 4n × n ≤ 234. Let us consider n as 5, now 45 x 5 = 225.

Step 6: Subtract 234 from 225; the remainder is 9, and the quotient is 25.

Step 7: Since the dividend is less than the divisor, add a decimal point and bring down two zeros to make it 900.

Step 8: Find the new divisor; 50 because 501 x 1 = 501.

Step 9: Subtract 501 from 900 to get a remainder of 399.

Step 10: The quotient is 25.1

Step 11: Continue these steps until you achieve the desired decimal precision.

So the square root of √634 is approximately 25.192