It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such square roots is infinite without any repeating pattern at all.

The square root of two is 1.41421356237309504880..., and the digital sum of the first one hundred decimal digits is 475.

For the first one hundred natural numbers, find the total of the digital sums of the first one hundred decimal digits for all the irrational square roots.

+-#Ratio
class Ratio
  include Comparable
  attr_reader :num, :den
  @@facts=[1]
  @@dfacts=[1,1]
  def initialize(a,b=1)
    neg=1
    neg*=-1 if a<0
    neg*=-1 if b<0
    e=Ratio.euc(a.abs,b.abs);
    @num=neg*(a.abs)/e
    @den=(b.abs)/e
  end
  def expand(digits=20)
    a=@num.abs
    b=@den
    str=""
    str="-" if @num<0
    str+=(a/b).to_s+"."
    1.upto(digits) do
      a=10*(a%b)
      str+=(a/b).to_s
    end
    str
  end
  def to_s()
    @num.to_s+"/"+@den.to_s
  end
  def neg?
    @num<0
  end
  def *(o)
    if o.class==Fixnum or o.class==Bignum
      return Ratio.new(@num*o,@den)
    end
    return Ratio.new(@num*o.num,@den*o.den)
  end
  def **(o)
    if o.class==Fixnum
      ret=Ratio.new(1)
      mult=self
      bin=o.to_s(2)
      while(bin.length>0)
        ret*=mult if bin[-1].chr=="1"
        mult*=mult
        bin.chop!
      end
      return ret
    end
  end
  def /(o)
    if o.class==Fixnum or o.class==Bignum
      return Ratio.new(@num,@den*o)
    end
    return Ratio.new(@num*o.den,@den*o.num)
  end
  def +(o)
    if o.class==Fixnum or o.class==Bignum
      return self+Ratio.new(o,1)
    end
    return Ratio.new(@num*o.den+@den*o.num,@den*o.den)
  end
  def -(o)
    return self + (o*(-1))
  end
  def ==(o)
    return (self.den==o.den and self.num==o.num)
  end
  def <=>(b)
    a=self
    return 0 if a==b
    return -1 if(a.neg? and not b.neg?)
    return 1 if(b.neg? and not a.neg?)
    return (b*(-1))<=>(a*(-1)) if(b.neg? and a.neg?)
    c=a-b
    return -1 if c.neg?
    1
  end

  def sqrt(iter)
    guess = self / 2
    iter.times do 
      guess = (guess+(self/guess))/2
    end
    guess
  end

  def Ratio.fromDecimal(str)
  #String should be of type "4783.9233r123"
    neg=Ratio.new(1)
    if(str[0].chr=="-")
      neg*=-1
      str=str[1..-1]
    end
    return neg*Ratio.new(str.to_i,1) if(str=~/^\d+$/)
    if(str=~/^(\d*)\.(\d+)$/)
      whole=$1.to_i
      part=$2
      whole=whole*(10**(part.length))+part.to_i
      return neg*Ratio.new(whole,10**(part.length))
    elsif(str=~/^(\d*)\.(\d*)r(\d+)$/)
      whole=0
      whole=$1.to_i if $1.length>0
      part=0
      part=$2.to_i if $2.length>0
      rep=$3.to_i
      den=1
      if($2.length>0)
        whole=whole*(10**$2.length)+part
        den=10**$2.length
      end
      subtract=whole
      whole=whole*(10**$3.length)+rep
      whole-=subtract
      den*=(10**$3.length)-1
      return neg*Ratio.new(whole,den)
    end
  end

  protected
  def num=(a)
    @num=a
  end
  def den=(b)
    @den=b
  end
  private
  def Ratio.euc(a,b)
    while b!=0
      a,b=b,a%b
    end
    a
  end
end

+-#Enumerable
module Enumerable
  def sum
    self.inject{|u,v|u+v}
  end
  def product
    self.inject{|u,v|u*v}
  end
  def count(ob)
    self.select{|i|i==ob}.length
  end
  def take_while
    return [] unless yield(self.first)
    if(self.class==Range)
      evalPoint=self.first
      evalPoint=evalPoint.succ while yield(evalPoint.succ) and not evalPoint==self.last
      return self.first..evalPoint
    else
      s=self.to_a
      upTo=1
      upTo+=1 while yield(s[upTo]) and upTo<self.length
      return self[0...upTo]
    end
  end
end

def p80
  nums=(1..100).to_a-(1..10).map{|i|i*i}
  puts nums.map{|i|Ratio.new(i).sqrt(10).expand(100)[0..100].split("").map{|j|j.to_i}.sum}.sum
end