Square Root of 1185
2026-02-28 09:50 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1185

The long division method is particularly used for non-perfect square numbers. In this method, we find the closest perfect square number to 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 1185, we need to group it as 11 and 85.

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 85, which is the new dividend. Add the old divisor with the same number 3 + 3, which gives us 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, where we need to find the value of n.

Step 5: The next step is finding 6n x n ≤ 285. Let's consider n as 4, hence 64 x 4 = 256.

Step 6: Subtract 256 from 285, the difference is 29, and the quotient becomes 34.

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 2900.

Step 8: Now we need to find the new divisor. Let's consider n as 4, so 688 x 4 = 2752.

Step 9: Subtract 2752 from 2900, we get the result 148.

Step 10: Now the quotient is 34.4.

Step 11: Continue these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.

So the square root of √1185 ≈ 34.44.