How do you find the square root of 85?

##sqrt85## is a non-terminating, non-repeating decimal. You can’t finish finding it. But you can get better and better approximations by: start with a number whose square is close to 85. (9 or 10. ##9^2## is closer, so start there.

Now divide 85 by ##9## to get ##9.4444## (to 4 places) Average the two numbers ##9## and ##9.4444## ##(9+9.4444)/2=9.2222##

Repeat: ##85-:9.2222=9.2169## (rounded to 4 places) Average: ##(9.2222+9.2169)/2=9.2196##

Repeat: ##85-:9.2196=9.2195## (rounded to 4 places) Average: ##(9.2196+9.2195)/2=9.2196##

##sqrt85~~9.2196##

That answer is accurate to 4 decimal places. If you need more accuracy, keep more decimal places at each step.