Square Root of 1404
2026-02-28 08:17 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1404

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 1404, we need to group it as 14 and 04.

Step 2: Now we need to find n whose square is less than or equal to 14. We can say n is '3' because 3 x 3 = 9, which is less than 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.

Step 3: Bring down 04, making the new dividend 504. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

Step 4: The new divisor will be 6n. We need to find n such that 6n × n ≤ 504. Let us consider n as 8. Now, 68 x 8 = 544.

Step 5: Since 544 is greater than 504, we try n as 7. So, 67 x 7 = 469, which is less than 504.

Step 6: Subtract 469 from 504. The difference is 35, and the quotient is 37.

Step 7: Since the remaining dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 3500.

Step 8: Find the new divisor: 746 x 4 = 2984.

Step 9: Subtracting 2984 from 3500 gives 516.

Step 10: The quotient is now 37.4.

Step 11: Continue doing these steps until we achieve the desired level of precision.

Thus, the square root of √1404 is approximately 37.48.