Square Root of 682
2026-02-28 09:13 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-682

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 682, we need to group it as 82 and 6.

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

Step 3: Bring down 82, making the new dividend 282. Add the old divisor (2) to itself to get 4, which will be part of our new divisor.

Step 4: The new divisor will be 4n. We need to find the value of n such that 4n × n ≤ 282. Let n be 6, then 46 × 6 = 276.

Step 5: Subtract 276 from 282, getting a remainder of 6, and the quotient is 26.

Step 6: Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend, making it 600.

Step 7: The new divisor becomes 52. We find n such that 52n × n ≤ 600. Suppose n is 1, then 521 × 1 = 521.

Step 8: Subtract 521 from 600, the difference is 79.

Step 9: Continue this process to achieve the desired decimal places.

So the square root of √682 ≈ 26.0998.