Marius Vollmer <marius.vollmer@uni-dortmund.de> writes:
>
>   (sqrt 4) => 2 (exact)
>
> I'm not sure whether exact square roots are imortant: they will only
> be useful when both the numerator and denominator are squares of
> integers and those pairs will be rare, I'd say.

I'd wondered if some sort of isqrt or isqrt+remainder would be of more
value to those wanting integer roots.  (Though I'm aware r5rs says
exact results for exact perfect squares is desirable.)

> We could use GMP for
> computing bignum square roots...

Rob mentioned this to me at one stage, I actually started on an
attempt at it.  Code below, which might sort of work, maybe.

One concern though is to ensure the root calculated is the same for a
"double" input (which uses sqrt()) as compared to some bignum root
(using gmp + conversions).