Square Root of 22.3
2026-02-28 10:31 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-22.3

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, group the numbers from right to left. In the case of 22.3, consider it as 22 and 3.

Step 2: Find n whose square is less than or equal to 22. We can say n is 4 because 4 × 4 = 16 is less than 22. Now the quotient is 4, after subtracting 16 from 22, the remainder is 6.

Step 3: Bring down 30 (since we need to consider the decimal and add two zeros), making the new dividend 630.

Step 4: The new divisor will be twice the quotient obtained, which is 8. Consider 8n as the new divisor and find n such that 8n × n is less or equal to 630.

Step 5: Consider n as 7, now 87 × 7 = 609.

Step 6: Subtract 609 from 630, the difference is 21, and the quotient is 4.7.

Step 7: Since the remainder is 21 and less than the divisor, add another pair of zeros to the dividend, making it 2100.

Step 8: The new divisor is 94, as 947 × 7 = 6629, which is too large, so use 946 × 6 = 5676.

Step 9: Continue this process to refine the quotient to 4.7202.