Locating Square Root of 2
To locate the square root of 2, we can use the method of approximation.

1. Guess and Check Method
- Start by making an initial guess. Let's say we start with 1 as our guess.
- Square the guess to see if it is close to 2. In this case, 1 squared is 1, which is less than 2.
- Increase the guess slightly and square it again. For example, if we try 1.5, 1.5 squared is 2.25, which is greater than 2.
- Continue this process, adjusting your guess each time until you find a number that when squared is close to 2.

2. Using Long Division Method
- Start by writing 2 as 2.0000, with the decimal point and extra zeros to the right.
- Divide the number into pairs of digits, starting from the decimal point. For 2.0000, we have 20, 00, 00.
- Find the largest number whose square is less than or equal to the first pair of digits. In this case, the largest number whose square is less than or equal to 20 is 4 (4 squared is 16).
- Bring down the next pair of zeros and double the number you found earlier (4) to get 8.
- Try to find a number to place after 8 such that when you subtract the resulting square from the remaining digits, you get as close to 0 as possible.
By following these methods, you can locate the square root of 2 with a reasonable level of accuracy.