Square Root of 1121
2026-02-28 08:40 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1121

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 1121, we need to group it as 21 and 11.

Step 2: Now we need to find n whose square is less than or equal to 11. We can say n as '3' because 3 x 3 = 9 is less than 11. Now the quotient is 3, and after subtracting 9 from 11, the remainder is 2.

Step 3: Now let us bring down 21, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 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 ≤ 221. Let's consider n as 3. Now, 63 x 3 = 189.

Step 6: Subtract 189 from 221; the difference is 32, and the quotient is 33.

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 3200.

Step 8: Now we need to find the new divisor and quotient. Using approximation, we get 334 x 4 = 1336.

Step 9: Subtracting 1336 from 3200, we get the result 1864.

Step 10: Now the quotient is 33.4.

Step 11: Continue doing these steps until we get two decimal places. So the approximate square root of √1121 is 33.487.