Question

What is `sqrt(83)`?

Answer 1

`sqrt(83) ~~ 9.11043358`

Explanation:

`sqrt(83)` is an irrational number satisfying `sqrt(83)*sqrt(83) = 83`

Since `83` is a prime number, it has no square factors and `sqrt(83)` cannot be simplified.

It is not a whole number and cannot be represented in the form `p/q` for integers `p` and `q`.

In decimal form it is approximately `9.11043358`

It can be expressed as a simple continued fraction

`sqrt(83) = [9;bar(9, 18)] = 9+1/(9+1/(18+1/(9+1/(18+1/(9+1/(18+...))))))`

You can use this continued fraction to calculate approximations for `sqrt(83)` by truncating it.

For example, `sqrt(83) ~~ [9;9] = 9+1/9 = 9.111bar(1)`

For more accurate approximations, truncate later:

`sqrt(83) ~~ [9;9,18] = 9+1/(9+1/18) = 9+18/163 ~~ 9.11043`