Square Root of 1189
2026-02-28 01:23 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1189

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 1189, we group it as 89 and 11.

Step 2: Now, we need to find n whose square is less than or equal to the leftmost group. For 11, n is 3 because 3 x 3 = 9 which is less than 11. The quotient is 3 and the remainder is 11 - 9 = 2.

Step 3: Bring down the next pair 89, making the new dividend 289. Add the old divisor with the same number 3 + 3 to get 6 as the new divisor.

Step 4: Find n such that 6n x n is less than or equal to 289. Let n be 4, then 64 x 4 = 256.

Step 5: Subtract 256 from 289; the difference is 33, and the quotient is 34.

Step 6: Since the dividend is less than the divisor, add a decimal point to the quotient. Adding the decimal point allows us to bring down two zeroes, making the new dividend 3300.

Step 7: Find a new divisor. The divisor is now 34 + 34 = 68. Find n such that 68n x n ≤ 3300. Let n be 4, then 684 x 4 = 2736.

Step 8: Subtract 2736 from 3300, resulting in 564.

Step 9: Bring down another pair of zeroes, making the dividend 56400.

Step 10: Continue this process.

The square root of 1189 is approximately 34.49.