You can turn them back into rationals, (rational (sqrt 2d0)) => 6369051672525773/4503599627370496

Or write your own operations that compute to the precision you want.

My post already covered inexact->exact:

     scheme@(guile-user)> (inexact->exact (sqrt 2.0))

$1 = 6369051672525773/4503599627370496

s9 Scheme fails on this as it's an irrational number, but the rest of Schemes such as STKlos, Guile, Mit Scheme, will do it right.

With Forth (and even EForth if the images it's compiled with FP support), you are on your own to check (or rewrite) an fsqrt function with an arbitrary precision.

Also, on trig, your parent commenter should check what CORDIC was.

https://en.wikipedia.org/wiki/CORDIC

If you want high precision trig functions on rationals, nothing's stopping you from writing a Taylor series library for them. Or some other polynomial appromation or a lookup table or CORDIC.

Check CORDIC, please.

https://en.wikipedia.org/wiki/CORDIC

Also, on sqrt functions, even a FP-enabled toy EForth under the Subleq VM (just as a toy, again, but it works) provides some sort of fsqrt functions:

    2 f fsqrt f.
    1.414 ok

Under PFE Forth, something 'bigger':

   40 set-precision ok  
   2e0 fsqrt f. 1.4142135623730951454746218587388284504414 ok 

EForth's FP precision it's tiny but good enough for very small microcontrollers. But it wasn't so far from the exponents the 80's engineers worked to create properly usable machinery/hardware and even software.