Square Root of 2349
2026-02-28 19:09 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2349

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 2349, we need to group it as 49 and 23.

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 is less than or equal to 23. Now the quotient is 4. After subtracting 23 - 16, the remainder is 7.

Step 3: Now let us bring down 49, which is the new dividend. Add the old divisor with the same number, 4 + 4, we get 8, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 8n × n ≤ 749. Let us consider n as 9. Now 89 x 9 = 801, which is too large. Instead, try n as 8, then 88 x 8 = 704.

Step 6: Subtract 749 from 704, the difference is 45, and the quotient is 48.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4500.

Step 8: Now we need to find the new divisor. Try 485, because 485 x 9 = 4365.

Step 9: Subtracting 4365 from 4500, we get the result 135.

Step 10: Now the quotient is 48.4.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √2349 ≈ 48.469