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#author("2026-07-05T06:12:19+09:00;2023-02-23T23:33:35+09:00","default:vip","vip")
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[[問題文>練習問題#r471e69d]]

解答例1
 import math, fractions
 
 N = 100
 
 squares = []
 for i in range(int(math.sqrt(N**2)), 1, -1):
     squares.append(i**2)
 
 simplifier = {}
 for n in range(2, N**2 + 1):
     if n in squares:
         simplifier[n] = (int(math.sqrt(n)), 1)
     else:
         x = 1
         y = n
         for s in squares:
             if y % s == 0:
                 y //= s
                 x *= int(math.sqrt(s))
         simplifier[n] = (x, y)
 
 for a in range(1, N+1):
     for b in range(2, N+1):  
         c = a * b
         integer, sqrt = simplifier[c]
         frac = fractions.Fraction(integer, b)
         numer, denom = frac.as_integer_ratio()
         if sqrt == 1:
             res = f"{frac}"
         elif frac == 1:
             res = f"√{sqrt}"
         elif numer == 1:
             res = f"√{sqrt}/{denom}"
         elif denom == 1:
             res = f"{numer}√{sqrt}"
         else:
             res = f"{numer}√{sqrt}/{denom}"
         print(f"√{a}/√{b} -> {res}")

解答例2
 from math import gcd
 from collections import defaultdict
 
 N = 100
 
 # √nの有理化
 # 答え: x√y
 def f1(n):
     p = n
     d = 2
     dic = defaultdict(int)
     while d * d <= p:
         while p % d == 0:
             dic[d] += 1
             p //= d
         d += 1
     if p > 1:
         dic[p] += 1
     x, y = 1, 1
     for p, e in dic.items():
         x *= p ** (e // 2)
         y *= p ** (e % 2)
     return x, y
 
 cache = {}
 
 def f2(n):
     if not n in cache:
         cache[n] = f1(n)
     return cache[n]
 
 for a in range(1, N+1):
     for b in range(2, N+1):
         # √a      xa√ya
         # --- = ----------
         # √b      xb√yb
         xa, ya = f2(a)
         xb, yb = f2(b)
         if yb > 1:
             ya *= yb
             xb *= yb
 #            yb = 1 #になる
             xxa, yya = f2(ya)
             xa *= xxa
             ya = yya
         g = gcd(xa, xb)
         xa //= g
         xb //= g
         # 分母が1
         if xb == 1:
             if ya == 1:
                 right = f'{xa}'
             elif xa == 1:
                 right = f'√{ya}'
             else:
                 right = f'{xa}√{ya}'
         # 分母がある
         else:
             if ya == 1:
                 right = f'{xa}/{xb}'
             elif xa == 1:
                 right = f'√{ya}/{xb}'
             else:
                 right = f'{xa}√{ya}/{xb}'
         print(f'√{a}/√{b} -> {right}')