square root of 2186 with full solution

Sure, let's calculate the square root of 2186 step by step.

1. Guess a number: The first step in finding the square root of a number is to make an initial guess. Let's guess that the square root of 2186 is around 45 (since 45^2 = 2025, which is close to 2186).

2. Divide and average: Next, divide the number you're trying to find the square root of (2186) by your guess (45). This gives you approximately 48.58. Now, take the average of this result and your original guess: (48.58 + 45) / 2 = 46.79. This is your new guess.

3. Repeat the process: Repeat the divide and average process with your new guess. So, divide 2186 by 46.79 to get approximately 46.75. Then, take the average of this result and your previous guess: (46.75 + 46.79) / 2 = 46.77.

4. Check for accuracy: Repeat the process until your guess is as accurate as you need it to be. In this case, repeating the process one more time gives us a guess of approximately 46.77, which is very close to the actual square root of 2186.

So, the square root of 2186 is approximately 46.77.