Question

How do you find the square root of 85?

Answer 1

`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.