Sometimes you have to improvise. If you have never heard of newton's method, binary search should probably come to mind next. It should be O(log N) which is a bit worse than constant-complexity square root but not too bad.

    DELTA = 0.0000001
    def sqrt_bin_search(squared_value, lower, higher)
      middle = (lower + higher) / 2.0
      if ((middle * middle) - squared_value).abs < DELTA
        middle
      elsif middle * middle > squared_value
        sqrt_bin_search(squared_value, lower, middle)
      else
        sqrt_bin_search(squared_value, middle, higher)
      end
    end

    def sqrt(x)
      sqrt_bin_search(x, 0, x)
    end