Square Root of 110
2026-02-28 23:48 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-110

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 110, we need to group it as 10 and 1.

Step 2: Now we need to find n whose square is ≤1. We can say n as ‘1’ because 1 × 1 is less than or equal to 1. Now the quotient is 1; after subtracting 1-1, the remainder is 0.

Step 3: Now let us bring down 10, which is the new dividend. Add the old divisor with the same number, 1 + 1; we get 2, which will be our new divisor.

Step 4: Now we get 2n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 10. Let us consider n as 4, now 2 × 4 × 4 = 32, which is more than 10. So, we take n as 3, then 2 × 3 × 3 = 18.

Step 6: Subtract 10 from 18, and the difference is -8, but since we can't have a negative remainder, review steps to ensure the closest n is chosen correctly.

Step 7: Add a decimal point to the quotient and bring down two zeros to the remainder, now making it 1000.

Step 8: The new divisor becomes 26 (2n + n = 23, add another n = 26). Choose n as 3, then 263 × 3 = 789.

Step 9: Subtracting 789 from 1000 gives us 211.

Step 10: Continue this process until you achieve the desired decimal precision.

The square root of √110 is approximately 10.4881.