{"id":1929,"date":"2025-12-24T17:21:22","date_gmt":"2025-12-24T08:21:22","guid":{"rendered":"https:\/\/math-travel.com\/?p=1929"},"modified":"2026-02-11T17:28:19","modified_gmt":"2026-02-11T08:28:19","slug":"double-radical-sign2","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-1\/double-radical-sign2\/","title":{"rendered":"\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9\uff01\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u300c\u5916\u305b\u306a\u3044\u6642\u300d\u306e\u5bfe\u51e6\u6cd5\u3092\u4f8b\u984c\u3067\u89e3\u8aac"},"content":{"rendered":"\n
\u4eca\u56de\u89e3\u6c7a\u3059\u308b\u60a9\u307f<\/span><\/div>
\n

\u300c\u30eb\u30fc\u30c8\u306e\u306a\u304b\u306b\u30eb\u30fc\u30c8\u304c\u3042\u308b\u300d <\/p>\n\n\n\n

\u300c\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9\u304c\u77e5\u308a\u305f\u3044\u300d<\/p>\n<\/div><\/div>\n\n\n\n

\u4eca\u56de\u306f\u6570\u2160\u306e\u300c\u6570\u3068\u5f0f\u300d\u304b\u3089\u3001\u4e8c\u91cd\u6839\u53f7\u306b\u3064\u3044\u3066\u306e\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u3066\u3044\u304f\u3088\uff01<\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9\u304c\u30a4\u30de\u30a4\u30c1\u5206\u304b\u3089\u306a\u304f\u3066\u3001\u305c\u3072\u6559\u3048\u3066\u6b32\u3057\u3044\u3067\u3059\u3002<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u4eca\u56de\u306f\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9\u306b\u3064\u3044\u3066\u8003\u3048\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n\n\n\n

\u307e\u305a\u306f\u3053\u3061\u3089\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\\[\\sqrt{5+2\\sqrt{6}}\u3001\\sqrt{5-2\\sqrt{6}}\\]<\/p>\n\n\n\n

\u30eb\u30fc\u30c8\u306e\u4e2d\u306b\u30eb\u30fc\u30c8\u304c\u3042\u3063\u3066\u3001\u521d\u3081\u3066\u898b\u305f\u4eba\u306f\u30d3\u30c3\u30af\u30ea\u3057\u307e\u3059\u3088\u306d<\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306f\u5916\u3057\u65b9\u306f\u516c\u5f0f\u3092\u77e5\u3089\u306a\u3044\u3068\u3001\u3053\u306e\u5f8c\u306e\u8a08\u7b97\u306b\u624b\u3082\u8db3\u3082\u51fa\u306a\u3044\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

\u7c21\u5358\u306a\u516c\u5f0f\u306a\u306e\u3067\u3001\u3053\u306e\u6a5f\u4f1a\u306b\u5fc5\u305a\u7fd2\u5f97\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9<\/span><\/div>
\n

\\(a>0,b>0\\)\u3068\u3059\u308b\u3068<\/p>\n\n\n\n

\\[\\sqrt{(a+b)+2\\sqrt{ab}}=\\sqrt{a}+\\sqrt{b}\\]<\/p>\n\n\n\n

\\(a>b>0\\)\u306e\u3068\u304d<\/p>\n\n\n\n

\\[\\sqrt{(a+b)-2\\sqrt{ab}}=\\sqrt{a}-\\sqrt{b}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u672c\u8a18\u4e8b\u3067\u306f\u3001”\u4e8c\u91cd\u6839\u53f7”\u306e\u5916\u3057\u65b9\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

2\u304c\u306a\u3044\u30d1\u30bf\u30fc\u30f3\u3084\u3001\u30de\u30a4\u30ca\u30b9\u306e\u4e8c\u91cd\u6839\u53f7\u306b\u3064\u3044\u3066\u3082\u89e3\u8aac\u3057\u3066\u308b\u306e\u3067\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u8d85\u57fa\u672c\u306a\u306e\u3067\u5fc5\u305a\u7406\u89e3\u3057\u3066\u304a\u3053\u3046\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u4e8c\u91cd\u6839\u53f7\u3068\u306f\uff1f<\/h2>\n\n\n\n

\u4eca\u56de\u89e3\u8aac\u3059\u308b”\u4e8c\u91cd\u6839\u53f7”\u3068\u3044\u3046\u306e\u306f\u3001\u30eb\u30fc\u30c8\u306e\u306a\u304b\u306b\u30eb\u30fc\u30c8\u304c\u3042\u308b\u3082\u306e\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\\[\\sqrt{5+2\\sqrt{6}}\u3001\\sqrt{5-2\\sqrt{6}}\\]<\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u89e3\u8aac\u3092\u3059\u308b\u524d\u306b\u3001\u300c\u6839\u53f7\u300d\u306b\u3064\u3044\u3066\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u6839\u53f7\u3068\u3044\u3046\u3068\u96e3\u3057\u3044\u3067\u3059\u304c\u3001\u30eb\u30fc\u30c8\\(\\sqrt{\u3000}\\)\u306e\u3053\u3068\u3092\u6307\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u6839\u53f7\u306e\u8a08\u7b97<\/span><\/div>
\n

\\[(\\sqrt{5})^{2}=5\\]<\/p>\n\n\n\n

\\[(-\\sqrt{5})^{2}=5\\]<\/p>\n\n\n\n

\\[-(\\sqrt{5})^{2}=-5\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u6839\u53f7\u306e\u4e2d\u8eab\u306b\u6587\u5b57\u304c\u5165\u3063\u3066\u3044\u308b\u3068\u304d\u306f\u3001\u6587\u5b57\u306e\u7b26\u53f7\u306b\u3088\u3063\u3066\u5834\u5408\u5206\u3051<\/span>\u304c\u5fc5\u8981\u3067\u3059\u3002<\/span><\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u540d\u524d\u306e\u3068\u304a\u308a2\u91cd\u306e\u6839\u53f7\u306b\u306a\u3063\u3066\u3044\u308b\u3063\u3066\u3053\u3068\u3067\u3059\u306d<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9<\/h2>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u3068\u306f\u3001\u30eb\u30fc\u30c8\u306e\u306a\u304b\u306b\u30eb\u30fc\u30c8\u304c\u3042\u308b\u3082\u306e\u3092\u6307\u3057\u3066\u3044\u307e\u3057\u305f<\/p>\n\n\n\n

\\[\\sqrt{5+2\\sqrt{6}}\u3001\\sqrt{5-2\\sqrt{6}}\\]<\/p>\n\n\n\n

\u3053\u306e\u307e\u307e\u3067\u306f\u8a08\u7b97\u304c\u96e3\u3057\u3059\u304e\u307e\u3059\u306d\u3002<\/p>\n\n\n\n

\u4ee5\u4e0b\u306e\u516c\u5f0f\u3092\u4f7f\u3046\u3053\u3068\u3067\u3001\u4e8c\u91cd\u6839\u53f7\u306f2\u3064\u306e\u30eb\u30fc\u30c8\u306b\u5f62\u3092\u5909\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9<\/span><\/div>
\n

\\(a>0,b>0\\)\u3068\u3059\u308b\u3068<\/p>\n\n\n\n

\\[\\sqrt{(a+b)+2\\sqrt{ab}}=\\sqrt{a}+\\sqrt{b}\\]<\/p>\n\n\n\n

\\(a>b>0\\)\u306e\u3068\u304d<\/p>\n\n\n\n

\\[\\sqrt{(a+b)-2\\sqrt{ab}}=\\sqrt{a}-\\sqrt{b}\\]<\/p>\n<\/div><\/div>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u516c\u5f0f\u3092\u898b\u305b\u3089\u308c\u3066\u3082\u30a4\u30de\u30a4\u30c1\u5206\u304b\u308a\u307e\u305b\u3093<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u5b9f\u969b\u306b\u4e8c\u91cd\u6839\u53f7\u3092\u5916\u3059\u904e\u7a0b\u3092\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u516c\u5f0f\u3060\u3051\u898b\u305b\u3089\u308c\u3066\u3082\u30d4\u30f3\u3068\u6765\u306a\u3044\u3067\u3059\u3088\u306d\u3002\u5b9f\u969b\u306b\u3001\u4e8c\u91cd\u6839\u53f7\u3092\u5916\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9<\/span><\/div>
\n

\\(a>0,b>0\\)\u3068\u3059\u308b\u3068<\/p>\n\n\n\n

\\[\\sqrt{(a+b)+2\\sqrt{ab}}=\\sqrt{a}+\\sqrt{b}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u307e\u305a\u306f\u52a0\u6cd5\u306e\u5f62\u3092\u3057\u305f\u4e8c\u91cd\u6839\u53f7\u3092\u5916\u3057\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

\u3053\u306e\u516c\u5f0f\u3092\u601d\u3044\u51fa\u3057\u3066\u3001\u8db3\u3057\u30668\u3001\u639b\u3051\u306615\u306b\u306a\u308b\u6570\u5b57\u306e\u7d44\u307f\u5408\u308f\u305b\u3092\u8003\u3048\u308b\u3068\u3001\\(a=5,b=3\\)\u306e\u7d44\u304c\u3042\u308a\u307e\u3059\u306d\u3002<\/p>\n\n\n\n

\u3088\u3063\u3066\u3001<\/p>\n\n\n\n

\\begin{eqnarray}
\\sqrt{8+2\\sqrt{15}}&=&\\sqrt{(5+3)+2\\sqrt{5\\cdot 3}}\\\\
&=&\\sqrt{5}+\\sqrt{3}
\\end{eqnarray}<\/p>\n\n\n\n

\u3053\u308c\u3067\u4e8c\u91cd\u6839\u53f7\u3092\u5916\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u540c\u69d8\u306e\u65b9\u6cd5\u3067\u3001\u6e1b\u6cd5\u306e\u5f62\u3092\u3057\u305f\u4e8c\u91cd\u6839\u53f7\u3082\u5916\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9<\/span><\/div>
\n

\\(a>b>0\\)\u306e\u3068\u304d<\/p>\n\n\n\n

\\[\\sqrt{(a+b)-2\\sqrt{ab}}=\\sqrt{a}-\\sqrt{b}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u3053\u306e\u5834\u5408\u306f\u3001\u8db3\u3057\u306612\u3001\u639b\u3051\u306635\u306b\u306a\u308b\u6570\u5b57\u306e\u7d44\u307f\u5408\u308f\u305b\u3092\u8003\u3048\u308b\u3068\u3001\\(a=7,b=5\\)\u306e\u7d44\u304c\u3042\u308a\u307e\u3059\u306d\u3002<\/p>\n\n\n\n

\u3088\u3063\u3066\u3001<\/p>\n\n\n\n

\\begin{eqnarray}
\\sqrt{12-2\\sqrt{35}}&=&\\sqrt{(7+5)-2\\sqrt{7 \\cdot 5}}\\\\
&=&\\sqrt{7}-\\sqrt{5}
\\end{eqnarray}<\/p>\n\n\n\n

\u3053\u308c\u3067\u6e1b\u6cd5\u306e\u4e8c\u91cd\u6839\u53f7\u3082\u5916\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u516c\u5f0f\u306f\u5206\u304b\u3063\u305f\u3051\u3069\u3001\u81ea\u5206\u3067\u3067\u304d\u308b\u304b\u306a\u3041\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u305f\u304f\u3055\u3093\u554f\u984c\u3092\u89e3\u3044\u3066\u6163\u308c\u3066\u3044\u304f\u3057\u304b\u306a\u3044\u306d<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u516c\u5f0f\u300a\u8a3c\u660e\u300b<\/h2>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9\u306e\u516c\u5f0f\u3092\u8a3c\u660e\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n\n\n\n

\u306a\u305c\u3053\u306e\u516c\u5f0f\u3067\u4e8c\u91cd\u6839\u53f7\u3092\u5916\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9<\/span><\/div>
\n

\\(a>0,b>0\\)\u3068\u3059\u308b\u3068<\/p>\n\n\n\n

\\[\\sqrt{(a+b)+2\\sqrt{ab}}=\\sqrt{a}+\\sqrt{b}\\]<\/p>\n\n\n\n

\\(a>b>0\\)\u306e\u3068\u304d<\/p>\n\n\n\n

\\[\\sqrt{(a+b)-2\\sqrt{ab}}=\\sqrt{a}-\\sqrt{b}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u8a3c\u660e<\/span><\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9\u3092\u8a3c\u660e\u3059\u308b\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u5c55\u958b\u306e\u516c\u5f0f\u304c\u30dd\u30a4\u30f3\u30c8\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u30dd\u30a4\u30f3\u30c8<\/span><\/div>
\n

\\[(a+b)^2=a^2+2ab+b^2\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u307e\u305a\u306f\u52a0\u6cd5\u306e\u4e8c\u91cd\u6839\u53f7\u306f\u3001<\/p>\n\n\n\n

\\begin{eqnarray}
\\sqrt{(a+b)+2\\sqrt{ab}}&=&\\sqrt{(\\sqrt{a}+\\sqrt{b})^{2}}\\\\
&=&|\\sqrt{a}+\\sqrt{b}|
\\end{eqnarray}<\/p>\n\n\n\n

\u3068\u306a\u308a\u3001\\(\\sqrt{a}\\)\u3082\\(\\sqrt{b}\\)\u3082\u6b63\u306e\u6570\u306a\u306e\u3067<\/p>\n\n\n\n

\\[|\\sqrt{a}+\\sqrt{b}|=\\sqrt{a}+\\sqrt{b}\\]<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

\\(a>0,b>0\\)\u3068\u3059\u308b\u3068<\/p>\n\n\n\n

\\[\\sqrt{(a+b)+2\\sqrt{ab}}=\\sqrt{a}+\\sqrt{b}\\]<\/p>\n\n\n\n

\u6e1b\u6cd5\u306e\u4e8c\u91cd\u6839\u53f7\u3082\u540c\u69d8\u306e\u8a3c\u660e\u3092\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\\begin{eqnarray}
\\sqrt{(a+b)-2\\sqrt{ab}}&=&\\sqrt{(\\sqrt{a}-\\sqrt{b})^{2}}\\\\
&=&|\\sqrt{a}-\\sqrt{b}|
\\end{eqnarray}<\/p>\n\n\n\n

\\(a>b>0\\)\u306a\u3089\u3070\u3001\\(\\sqrt{a}-\\sqrt{b}>0\\)\u304c\u6210\u308a\u7acb\u3064\u306e\u3067\u3001<\/p>\n\n\n\n

\\[|\\sqrt{a}-\\sqrt{b}|=\\sqrt{a}-\\sqrt{b}\\]<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001\\(a>b>0\\)\u306e\u3068\u304d<\/p>\n\n\n\n

\\[\\sqrt{(a+b)-2\\sqrt{ab}}=\\sqrt{a}-\\sqrt{b}\\]<\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u3060\u304b\u3089\u4e8c\u91cd\u6839\u53f7\u3092\u5916\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3093\u3067\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u4f59\u88d5\u304c\u3042\u308b\u4eba\u306f\u516c\u5f0f\u306e\u8a3c\u660e\u3082\u7406\u89e3\u3057\u3066\u304a\u3053\u3046<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

2\u304c\u306a\u3044\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9<\/h2>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u8a08\u7b97\u306b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u3082\u306e\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n

\n
\"\uff12\u304c\u306a\u3044\u4e8c\u91cd\u6839\u53f7\u3068\u306f\uff1f\"<\/figure>\n<\/div>\n\n\n

\u524d\u534a\u90e8\u5206\u3067\u7d39\u4ecb\u3057\u305f\u4e8c\u91cd\u6839\u53f7\u3068\u3069\u3053\u304c\u7570\u306a\u308b\u304b\u5206\u304b\u308a\u307e\u3059\u304b\uff1f<\/p>\n\n\n

\n
\"2\u304c\u306a\u3044\u4e8c\u91cd\u6839\u53f7\u306e\u56f3\"
\u300a2\u304c\u306a\u3044\u4e8c\u91cd\u6839\u53f7\u300b<\/figcaption><\/figure>\n<\/div>\n\n\n

\u3053\u3046\u3044\u3063\u305f\u4e8c\u91cd\u6839\u53f7\u3092\u5916\u3059\u306b\u306f\u5de5\u592b\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n

2\u3092\u4f5c\u308b\u30d1\u30bf\u30fc\u30f3<\/h3>\n\n\n\n
2\u3092\u4f5c\u308b\u30d1\u30bf\u30fc\u30f3<\/span><\/div>
\n

\u6b21\u306e\u5f0f\u3092\u7c21\u5358\u306b\u305b\u3088\u3002<\/p>\n\n\n\n

\\[\\sqrt{4+\\sqrt{15}}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306f\u8db3\u3057\u3066A\u306e\u90e8\u5206\u3001\u639b\u3051\u3066B\u306e\u90e8\u5206\u306b\u306a\u308b\u3001\\(a,b\\)\u306e\u7d44\u307f\u5408\u308f\u305b\u3092\u63a2\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u3057\u304b\u3057\u3001\u3053\u306e\u307e\u307e\u3060\u3068B\u306e\u6839\u53f7\u306e\u524d\u306b\uff12\u304c\u306a\u3044\u306e\u3067\u7121\u7406\u3084\u308a\u5f0f\u5909\u5f62\u3092\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\\begin{eqnarray}
\\displaystyle \\sqrt{4+\\sqrt{15}}&=&\\sqrt{\\frac{8+2\\sqrt{15}}{2}}\\\\
\\displaystyle &=&\\frac {\\sqrt{8+2\\sqrt{15}}}{\\sqrt{2}}\\\\
\\displaystyle &=&\\frac {\\sqrt{3}+\\sqrt{5}}{\\sqrt{2}}\\\\
\\displaystyle &=&\\frac {\\sqrt{6}+\\sqrt{10}}{2}
\\end{eqnarray}<\/p>\n\n\n\n

\u3053\u308c\u3067\u4e8c\u91cd\u6839\u53f7\u3092\u5916\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

2\u306b\u306a\u308b\u3088\u3046\u306b\u8abf\u6574\u3059\u308b\u30d1\u30bf\u30fc\u30f3<\/h3>\n\n\n\n
2\u3092\u306a\u308b\u3088\u3046\u306b\u8abf\u6574\u3059\u308b\u30d1\u30bf\u30fc\u30f3<\/span><\/div>
\n

\u6b21\u306e\u5f0f\u3092\u7c21\u5358\u306b\u305b\u3088\u3002<\/p>\n\n\n\n

\\[\\sqrt{14-6\\sqrt{5}}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u6839\u53f7\u306e\u4fc2\u6570\u304c6\u306a\u306e\u3067\u30012\u306b\u306a\u308b\u3088\u3046\u306b\u8abf\u6574\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\\[\\sqrt{14-6\\sqrt{5}}=\\sqrt{14-2\\sqrt{45}}\\]<\/p>\n\n\n\n

\u3053\u3046\u306a\u3063\u3066\u3057\u307e\u3048\u3070\u3001\u4e8c\u91cd\u6839\u53f7\u306e\u516c\u5f0f\u306b\u5f53\u3066\u306f\u3081\u3066\u3001<\/p>\n\n\n\n

\u8db3\u3057\u306614\u3001\u639b\u3051\u306645\u306b\u306a\u308b\u6570\u306e\u7d44\u307f\u5408\u308f\u305b\u306f\u3001\\((a,b)=(9,5)\\)<\/p>\n\n\n\n

\\begin{eqnarray}
\\sqrt{14-6\\sqrt{5}}&=&\\sqrt{14-2\\sqrt{45}}\\\\
&=&\\sqrt{9}-\\sqrt{5}\\\\
&=&3-\\sqrt{5}
\\end{eqnarray}<\/p>\n\n\n\n

\u3088\u3063\u3066\u3001\u4e8c\u91cd\u6839\u53f7\u3092\u5916\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u3092\u5916\u3059\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5f0f\u3092\u7c21\u5358\u306b\u3059\u308b\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u3092\u5916\u3059<\/span><\/div>
\n

\u6b21\u306e\u4e8c\u91cd\u6839\u53f7\u3092\u7c21\u5358\u306b\u3057\u3088\u3046\u3002<\/p>\n\n\n\n

\\((1) \\sqrt{7+2\\sqrt{10}}\\)<\/p>\n\n\n\n

\\((2) \\sqrt{5+\\sqrt{21}}\\)<\/p>\n\n\n\n

\\((3) \\sqrt{18+8\\sqrt{2}}\\)<\/p>\n<\/div><\/div>\n\n\n\n

(1)\u306e\u89e3\u8aac<\/h3>\n\n\n\n

\u3053\u308c\u306f\u4e8c\u91cd\u6839\u53f7\u306e\u516c\u5f0f\u304c\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b\u30d1\u30bf\u30fc\u30f3\u3067\u3059\u306d\u3002<\/p>\n\n\n\n

\\begin{eqnarray}
\\sqrt{7+2\\sqrt{10}}&=&\\sqrt{(5+2)+2\\sqrt{5 \\cdot 2}}\\\\
&=&\\sqrt{5}+\\sqrt{2}
\\end{eqnarray}<\/p>\n\n\n\n

(2)\u306e\u89e3\u8aac<\/h3>\n\n\n\n

\u3053\u308c\u306f2\u304c\u306a\u3044\u306e\u3067\u5de5\u592b\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n

\\begin{eqnarray}
\\displaystyle \\sqrt{5+\\sqrt{21}}&=&\\sqrt{\\frac{10+2\\sqrt{21}}{2}}\\\\
\\displaystyle &=&\\frac{\\sqrt{10+2\\sqrt{21}}}{\\sqrt{2}}\\\\
\\displaystyle &=&\\frac{\\sqrt{7}+\\sqrt{3}}{\\sqrt{2}}\\\\
\\displaystyle &=&\\frac{\\sqrt{14}+\\sqrt{6}}{2}
\\end{eqnarray}<\/p>\n\n\n\n

(3)\u306e\u89e3\u8aac<\/h3>\n\n\n\n

\u3053\u308c\u306f2\u3092\u3064\u304f\u308b\u5de5\u592b\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n

\\begin{eqnarray}
\\displaystyle \\sqrt{18+8\\sqrt{2}}&=&\\sqrt{18+2\\sqrt{32}}\\\\
\\displaystyle &=&\\sqrt{16}+\\sqrt{2}\\\\
\\displaystyle &=&4+\\sqrt{2}\\\\
\\end{eqnarray}<\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u3092\u4f7f\u3046\u3068\u3001\u7c21\u5358\u306a\u5f62\u306b\u5909\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9<\/span><\/div>
\n

\\(a>0,b>0\\)\u3068\u3059\u308b\u3068<\/p>\n\n\n\n

\\[\\sqrt{(a+b)+2\\sqrt{ab}}=\\sqrt{a}+\\sqrt{b}\\]<\/p>\n\n\n\n

\\(a>b>0\\)\u306e\u3068\u304d<\/p>\n\n\n\n

\\[\\sqrt{(a+b)-2\\sqrt{ab}}=\\sqrt{a}-\\sqrt{b}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u516c\u5f0f\u306f\u7c21\u5358\u306a\u306e\u3067\u305f\u304f\u3055\u3093\u554f\u984c\u3092\u89e3\u304d\u3001\u516c\u5f0f\u306b\u6163\u308c\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u4eca\u56de\u306f\u6570\u2160\u306e\u300c\u6570\u3068\u5f0f\u300d\u304b\u3089\u3001\u4e8c\u91cd\u6839\u53f7\u306b\u3064\u3044\u3066\u306e\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u3066\u3044\u304f\u3088\uff01 \u4eca\u56de\u306f\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9\u306b\u3064\u3044\u3066\u8003\u3048\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002 \u307e\u305a\u306f\u3053\u3061\u3089\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002 \\[\\sqrt{5+2\\sqrt{6}}\u3001\\sqrt{5-2\\sqr […]<\/p>\n","protected":false},"author":1,"featured_media":6372,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[8,222],"tags":[9,10,11],"class_list":["post-1929","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-suushiki","category-math-1","tag-9","tag-a","tag-11"],"yoast_head":"\n\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9\uff01\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u300c\u5916\u305b\u306a\u3044\u6642\u300d\u306e\u5bfe\u51e6\u6cd5\u3092\u4f8b\u984c\u3067\u89e3\u8aac<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/math-travel.jp\/math-1\/double-radical-sign2\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9\uff01\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u300c\u5916\u305b\u306a\u3044\u6642\u300d\u306e\u5bfe\u51e6\u6cd5\u3092\u4f8b\u984c\u3067\u89e3\u8aac\" \/>\n<meta property=\"og:description\" content=\"\u4eca\u56de\u306f\u6570\u2160\u306e\u300c\u6570\u3068\u5f0f\u300d\u304b\u3089\u3001\u4e8c\u91cd\u6839\u53f7\u306b\u3064\u3044\u3066\u306e\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u3066\u3044\u304f\u3088\uff01 \u4eca\u56de\u306f\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9\u306b\u3064\u3044\u3066\u8003\u3048\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002 \u307e\u305a\u306f\u3053\u3061\u3089\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002 [sqrt{5+2sqrt{6}}\u3001sqrt{5-2sqr […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/math-travel.jp\/math-1\/double-radical-sign2\/\" \/>\n<meta property=\"og:site_name\" content=\"\u30de\u30b9\u30c8\u30e9\u9ad8\u6821\u6570\u5b66\u307e\u3068\u3081\u30b5\u30a4\u30c8\" \/>\n<meta property=\"article:published_time\" content=\"2025-12-24T08:21:22+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-02-11T08:28:19+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2020\/05\/\u4e8c\u91cd\u6839\u53f7\u306e\u5916\u3057\u65b9.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"630\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"\u3086\u3046\u3084\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@https:\/\/twitter.com\/mathtora\" \/>\n<meta name=\"twitter:label1\" content=\"\u57f7\u7b46\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u3086\u3046\u3084\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u63a8\u5b9a\u8aad\u307f\u53d6\u308a\u6642\u9593\" \/>\n\t<meta name=\"twitter:data2\" content=\"1\u5206\" \/>\n<script 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