When I try to run your code, I get an incorrect answer for the root. I think the problem is in the exponent. The exponents are $root and ($root - 1), respectively.

When I run this code:

timethese( 100, {
    'Root' => '$x = Root( 100, 3 )',
    'Root2' => '$y = Root2( 100, 3 )',
});

print <<END;

Root: $x
-----
Root2: $y
END
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I get this for output:

Benchmark: timing 100 iterations of Root, Root2...
      Root: 29 wallclock secs (28.39 usr +  0.00 sys = 28.39 CPU) @  3
+.52/s (n=1 00)
     Root2: 20 wallclock secs (20.03 usr +  0.00 sys = 20.03 CPU) @  4
+.99/s (n=1 00)

Root: 4.6415888336127788924100763542328778501807372125002714
-----
Root2: 0.6664902595019951166742874561807256134735
[download]

___________________
Kurt