Square Root of 1184
2026-02-28 01:29 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1184

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 1184, we need to group it as 84 and 11.

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

Step 3: Now let us bring down 84 which is the new dividend. 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 60 (6n), and we need to find the value of n.

Step 5: The next step is finding 60n × n ≤ 284; let us consider n as 4, now 60 x 4 = 240.

Step 6: Subtract 284 from 240, the difference is 44.

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 4400.

Step 8: Now we need to find the new divisor that is 698 because 698 x 6 = 4188.

Step 9: Subtracting 4188 from 4400, we get the result 212.

Step 10: Now the quotient is 34.4.

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 √1184 is approximately 34.409.