Add the same method to multiple classes

You'll want to use #class_eval:

classes = [Fixnum, Float]
classes.each do |x|
    x.class_eval do
        def root(pow)
            return self ** (1/pow.to_f)
        end
    end
end

See this blog post as a reference.

Alternatively, you could create a module and include it into each class:

module MyRoot
  def root(pow)
    return self ** (1/pow.to_f)
  end
end

class Fixnum
  include MyRoot
end

class Float
  include MyRoot
end

I lean towards the latter. It's clearer what you're doing and allows one-off additions as well.

The relevant part of the class hierarchy looks like this:

• Numeric
  • Integer
    • Older versions had Fixnum and Bignum as subclasses of Integer.
  • Float
  • Rational

So patch your change into Numeric to cover them all at once:

class Numeric
  def root(pow)
    return self ** (1/pow.to_f)
  end
end

Then you can do these things:

>> 11.root(2) # Integer
=> 3.3166247903554
>> 2.18.root(3) # Float
=> 1.296638256974172
>> Rational(23, 42).root(6) # Rational
=> 0.9045094132598528
>> 2**1000.root(42) # Integer
=> 2.2638347236157763