Calculating the Square Root of 82.6
To find the square root of 82.6, we can use a method called the long division method. This method involves breaking down the number into parts and finding the square root iteratively.

Step 1: Estimation
- Let's start by estimating the square root of 82.6. Since 9^2 = 81, we know that the square root of 82.6 is slightly greater than 9.

Step 2: Long Division Method
- To begin the long division method, we group the number 82.6 into pairs of digits from right to left. We have 82 and 60.

Step 3: Finding the Square Root
- Now, we take the largest number whose square is less than or equal to 82, which is 9. We subtract 81 from 82, leaving us with a remainder of 1. We bring down the next pair of digits, 60.
- Next, we double the quotient (9) to get 18. We then find the largest number that, when added to 18 as the tens digit of a new number, gives a product less than or equal to 160. This number is 8, as 188 * 8 = 1504.
- Subtracting 1504 from 1600 leaves us with a remainder of 96. We bring down the next pair of zeros and repeat the process.
- We continue this process until we have enough decimal places for our required accuracy.

Result
- The square root of 82.6 is approximately 9.09 when rounded to two decimal places.