Square Root of 2344
2026-02-28 11:01 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2344

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, we need to group the numbers from right to left. In the case of 2344, we need to group it as 23 and 44.

Step 2: Now we need to find n whose square is less than or equal to 23. We can say n is 4 because 4 x 4 = 16, which is less than 23. The quotient is 4, and after subtracting 16 from 23, the remainder is 7.

Step 3: Bring down 44 to form the new dividend, which is 744. Add the old divisor (4) to itself (4 + 4 = 8) to form the new divisor.

Step 4: Find n such that 8n x n ≤ 744. Let n be 9, then 89 x 9 = 801, which is greater than 744, so we try n = 8, 88 x 8 = 704, which fits.

Step 5: Subtract 704 from 744, leaving a remainder of 40. The quotient is now 48.

Step 6: Since the remainder is less than the divisor, and we need more precision, add a decimal point and bring down 00, making it 4000.

Step 7: Find the new divisor by doubling the current quotient (48) to get 96. Find n such that 96n x n ≤ 4000. Try n = 4, then 964 x 4 = 3856.

Step 8: Subtract 3856 from 4000, leaving a remainder of 144. The quotient is 48.4.

Step 9: Continue these steps until the desired precision is reached.

The approximation of √2344 is 48.42.