Square Root of 2268
2026-02-28 23:27 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2268

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 2268, we need to group it as 68 and 22.

Step 2: Now we need to find a number whose square is less than or equal to 22. We can say this number is 4 because 4 × 4 = 16, which is less than 22. Now the quotient is 4, and after subtracting 16 from 22, the remainder is 6.

Step 3: Bring down 68, making the new dividend 668. Add the old divisor (4) with the same number (4), getting 8, which will be our new divisor.

Step 4: The new divisor will be 8n, where we need to find n such that 8n × n ≤ 668.

Step 5: By trial, we find that 8 × 8 = 64, and 648 is close to 668. Subtracting gives us a remainder of 20, and the quotient becomes 46.

Step 6: Since the dividend is less than the divisor, we add a decimal point, allowing us to bring down two zeros, making the new dividend 2000.

Step 7: We find the new divisor to be 929, since 929 × 2 = 1858, which is less than 2000.

Step 8: Subtracting 1858 from 2000, we get a remainder of 142.

Step 9: Continue these steps until we get two numbers after the decimal point.

The square root of √2268 ≈ 47.62.