Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 The long<a>division</a>method is helpful for both perfect and non-perfect square numbers. Here, we will find the square root using the long division method, step by step.

2 Step 1:To begin with, we need to group the numbers from right to left. In the case of 11881, we group it as 11, 88, and 1.

3 Step 2:Now we need to find n whose square is<a>less than</a>or equal to 11. We can say n is 3 because 3 x 3 = 9, which is less than 11. Now the<a>quotient</a>is 3, and after subtracting 9 from 11, the<a>remainder</a>is 2.

4 Step 3:Bring down the next pair, which is 88, making the new<a>dividend</a>288. Add the old<a>divisor</a>with the same number, 3 + 3, to get 6, which will be part of our new divisor.

5 Step 4:The new divisor is 6n. We need to find n such that 6n x n is less than or equal to 288. We find n is 4 because 64 x 4 = 256, which is less than 288.

6 Step 5:Subtract 256 from 288; the difference is 32. The next digit in the quotient is 4.

7 Step 6:Bring down the next pair, which is 1, making the new dividend 321. Add the old divisor with the last digit of the quotient, 64 + 4, to get 68, which will be part of our new divisor.

8 Step 7:The new divisor is 68n. We need to find n such that 68n x n is less than or equal to 321. We find n is 1 because 681 x 1 = 681, which is<a>greater than</a>321.

9 Hence, n is 0, and the process has reached a conclusion with the quotient being 109. So the square root of √11881 is 109.