「数学ガールの秘密ノート」「第189回　九章算術の研究、もっと」より https://bit.ly/girlnote189

sqrtn.rb

def sqrtn(s)
  a = 0
  p = 0
  while not (0 <= (s / 10**p) and (s / 10**p) < 100) do
    p += 2
  end
  while p >= 0
    b = 9
    while (s / 10**p) < b * (20 * a + b) do
      b -= 1
    end
    s = s - b * (20 * a + b) * 10**p
    a = 10 * a + b
    p -= 2
  end
  return a
end

def test_sqrtn
  (0..99999).each do |n|
    a = sqrtn(n)
    b = Math::sqrt(n).to_i
    if a == b
      puts "OK: sqrtn(#{n}) is #{a}. (#{Math::sqrt(n)})"
    else
      puts "ERROR: sqrtn(#{n}) is #{a}, but Math::sqrt(n).to_i is #{b} (#{Math::sqrt(n)})"
      abort
    end
  end
end

puts sqrtn(55225)
puts sqrtn(3972150625)
puts sqrtn(2_00_00_00_00_00_00_00_00)
# test_sqrtn