Calculating the square root of 10
To find the square root of 10 correct to 4 decimal places, we can use the method of approximation.

Guess a number
- Let's start by guessing a number that when squared is close to 10. A good initial guess could be 3, as 3 squared is 9, which is close to 10.

Improve the guess
- To improve our guess, we can use the formula:
Guess = (Guess + (10 / Guess)) / 2
Applying this formula multiple times will bring us closer to the actual square root of 10.

Calculating the square root
- Starting with our initial guess of 3:
Guess 1 = (3 + (10 / 3)) / 2 = (3 + 3.3333) / 2 = 6.3333 / 2 = 3.1667
Guess 2 = (3.1667 + (10 / 3.1667)) / 2 ≈ 3.1960
Guess 3 = (3.1960 + (10 / 3.1960)) / 2 ≈ 3.1623
Guess 4 = (3.1623 + (10 / 3.1623)) / 2 ≈ 3.1623
Therefore, the square root of 10 correct to 4 decimal places is approximately 3.1623.