Square Root of 1412
2026-02-28 00:58 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1412

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 1412, we need to group it as 12 and 14.

Step 2: Now, we need to find n whose square is less than or equal to 14. We can say n as ‘3’ because 3 × 3 = 9 is lesser than 14. Now the quotient is 3. After subtracting 9 from 14, the remainder is 5.

Step 3: Now, let us bring down 12 which is the new dividend. Add the old divisor with the same number 3 + 3, we get 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 512. Let us consider n as 8. Now, 68 × 8 = 544

Step 6: Since 544 is greater than 512, we consider n as 7. Therefore, 67 × 7 = 469

Step 7: Subtract 469 from 512; the difference is 43. The quotient is 37.

Step 8: 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 4300.

Step 9: Now, we need to find the new divisor, which is 754 because 754 × 4 = 3016

Step 10: Subtracting 3016 from 4300, we get the result 1284.

Step 11: The quotient is now 37.4. Step 12: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.

So, the square root of √1412 is approximately 37.558.