Babylonian method
Step 1 -- Take the square root you're trying to find, square it, and divide by your guess.
\(\sqrt{130}^2 = 130 \\\\ \frac{130}{11.4022} = 11.4013085\)
Step 2 -- Find the average between your guess and the new number.
\(\frac{11.4013085+11.4022}2=\boxed{11.40175425}\)
