Square Root of 1409
2026-02-28 23:33 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1409

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 1409, we need to group it as 09 and 14.

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

Step 3: Now let us bring down 09 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, we need to find the value of n.

Step 5: The next step is finding 6n x n ≤ 509 let us consider n as 8, now 6 x 8 x 8 = 384

Step 6: Subtract 509 from 384 the difference is 125, and the quotient is 38.

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 12500.

Step 8: Now we need to find the new divisor that is 759 because 759 x 9 = 6831.

Step 9: Subtracting 6831 from 12500 we get the result 5669.

Step 10: Now the quotient is 37.5.

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 √1409 is approximately 37.53.