Square Root of 1180
2026-02-28 23:35 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1180

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 1180, we need to group it as 80 and 11.

Step 2: Now we need to find n whose square is closest 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, and after subtracting 9 from 11, the remainder is 2.

Step 3: Now let us bring down 80, which is the new dividend. Add the old divisor with the same number 3 + 3 = 6, which will be our new divisor.

Step 4: With 6 as the new divisor, we need to find the value of n such that 6n x n ≤ 280.

Step 5: The next step is finding n such that 6n x n ≤ 280. Let us consider n as 4. Now, 64 x 4 = 256.

Step 6: Subtract 256 from 280; the difference is 24, and the quotient is 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 2400.

Step 8: Now we need to find the new divisor. Let’s consider n as 3 because 683 x 3 = 2049.

Step 9: Subtracting 2049 from 2400, we get the result 351.

Step 10: Now the quotient is 34.3

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.

So the square root of √1180 is approximately 34.38.