Square Root of 662
2026-02-28 11:23 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-662

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 662, we group it as 62 and 6.

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

Step 3: Bring down 62, making the new dividend 262. Add the old divisor (2) to itself, giving us 4, which will be our new divisor.

Step 4: The next step is finding 4n × n ≤ 262. Let us consider n as 6, now 4 × 6 × 6 = 144.

Step 5: Subtract 144 from 262; the difference is 118.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point, allowing us to add two zeroes to the dividend. Now the new dividend is 11800.

Step 7: Find the new divisor, which is 45, because 457 × 7 = 3199.

Step 8: Subtracting 3199 from 11800, we get 8601.

Step 9: Now the quotient is 25.7.

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.

So the square root of √662 is approximately 25.73.