You might also try this :

sub Root2 {
my $num        = shift;
my $root       = shift;
my $iterations = shift || 10;
if ( $root == 0 ) { return 1 }
if ( $num < 0 ) { return undef }
my $current = Math::BigFloat->new();
my $guess   = Math::BigFloat->new( $num / $root );
my $t=Math::BigFloat->new($guess**($root-1)); 1st version : WRONG ! sh
+ould be in the loop.
for ( 1 .. $iterations ) {
        $current = $guess - ( $guess * $t - $num ) / ( $root * $t  );
    if ( $guess eq $current ) { last }
    $t=Math::BigFloat->new($current**($root-1));
    $guess = $current;
}
return $current;
}
[download]

The idea behind, is that '**' is MUCH slower than '*', so I exchange 2 '**' for one '**' and 2 '*'
It seems indeed to speed things alot :
(I'm sure your numerous tests will make it sure ;-)

timethese(10,{
    'Root'=> sub {Root(1000,60)},
    'Root2'=> sub {Root2(1000,60)}});
[download]

gives as result :

  Benchmark: timing 10 iterations of Root, Root2...
    Root: 104 wallclock secs (104.38 usr + 0.01 sys = 104.39 CPU) @ 0.10/s (n=10)
    Root2: 15 wallclock secs (14.75 usr + 0.00 sys = 14.75 CPU) @ 0.68/s (n=10)
    Root2: 97 wallclock secs (92.67 usr + 0.16 sys = 92.83 CPU) @ 0.11/s (n=10)

UPDATE :
Corrected my code! I misplaced the $t calculation outside the loop,
which is wrong beccause $guess change inside the loop.
As you can see it's no more so fast...

"Only Bad Coders Code Badly In Perl" (OBC2BIP)