日本文教出版：中学数学３

p.42 問1　\(1.41^2=1.9881\)
　\(1.42^2=2.0164\)
これと \(x^2=2\) より、
　\(1.41^2< x^2 < 1.42^2\)
よって、
　\(1.41< x < 1.42\)

p.43 問2　\(1.73\)

p.43 問3\(\begin{split}{\small (1)}~5\end{split}\)　　\(\begin{split}{\small (2)}~\sqrt{5}\end{split}\)　　\(\begin{split}{\small (3)}~2.24\end{split}\)

p.44 問1\(\begin{split}{\small (1)}~\pm\,6\end{split}\)　　\(\begin{split}{\small (2)}~\pm\,7\end{split}\)　　\(\begin{split}{\small (3)}~\pm\,1\end{split}\)

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\(\begin{split}{\small (4)}~\pm\,0.4\end{split}\)　　\(\begin{split}{\small (5)}~\pm\,\frac{\,1\,}{\,3\,}\end{split}\)　　\(\begin{split}{\small (6)}~0\end{split}\)

p.45 問2\(\begin{split}{\small (1)}~\pm\,\sqrt{10}\end{split}\)　　\(\begin{split}{\small (2)}~-\sqrt{6}\end{split}\)

p.45 問3\(\begin{split}{\small (1)}~6\end{split}\)　　\(\begin{split}{\small (2)}~13\end{split}\)　　\(\begin{split}{\small (3)}~0.5\end{split}\)

p.45 問4\(\begin{split}{\small (1)}~9\end{split}\)　　\(\begin{split}{\small (2)}~7\end{split}\)　　\(\begin{split}{\small (3)}~12\end{split}\)

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\(\begin{split}{\small (4)}~-6\end{split}\)　　\(\begin{split}{\small (5)}~\frac{\,3\,}{\,4\,}\end{split}\)

p.47 問1\(\begin{split}{\small (1)}~\sqrt{13}>\sqrt{11}\end{split}\)　　\(\begin{split}{\small (2)}~\sqrt{24}< 5\end{split}\)
\(\begin{split}{\small (3)}~-\sqrt{8}>-\sqrt{10}\end{split}\)　　\(\begin{split}{\small (4)}~\sqrt{0.1}>0.1\end{split}\)

p.47 問2　\(\sqrt{10}~,~\sqrt{13}\)

p.47 問3　Ａ：\(-\sqrt{11}\)、Ｂ：\(-\sqrt{0.5}\)

　Ｃ：\(\begin{split}\sqrt{\frac{\,2\,}{\,3\,}}\end{split}\)、Ｄ：\(\sqrt{17}\)

p.49 問1

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有理数は、\(\begin{split}0.2~,~-\frac{\,1\,}{\,8\,}~,~\sqrt{49}~,~\sqrt{\frac{\,4\,}{\,9\,}}~,~0\end{split}\)

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無理数は、\(\begin{split}\sqrt{6}~,~-\sqrt{5}\end{split}\)

p.49 問2\(\begin{split}{\small (1)}~\end{split}\)アは有限小数、イは無限小数
\(\begin{split}{\small (2)}~\end{split}\)いくつかの数字を決まった順にくり返す

p.50 基本の問題 1\(\begin{split}{\small (1)}~-8~,~-8\end{split}\)
\(\begin{split}{\small (2)}~6~,~-6~,~6~,~-6\end{split}\)

p.50 基本の問題 2\(\begin{split}{\small (1)}~14\end{split}\)　　\(\begin{split}{\small (2)}~15\end{split}\)

p.50 基本の問題 3\(\begin{split}{\small (1)}~2\end{split}\)　　\(\begin{split}{\small (2)}~3\end{split}\)

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\(\begin{split}{\small (3)}~16\end{split}\)　　\(\begin{split}{\small (4)}~\frac{\,5\,}{\,3\,}\end{split}\)

p.50 基本の問題 4\(\begin{split}{\small (1)}~-\sqrt{2}< 0\end{split}\)　　\(\begin{split}{\small (2)}~\sqrt{5}<\sqrt{10}\end{split}\)
\(\begin{split}{\small (3)}~3<\sqrt{11}\end{split}\)　　\(\begin{split}{\small (4)}~5>\sqrt{21}\end{split}\)

p.50 基本の問題 5　\(10\) 個

p.50 基本の問題 6\(\begin{split}{\small (1)}~3~,~2.6~,~\sqrt{7}\end{split}\)
\(\begin{split}{\small (2)}~3~,~0~,~-\sqrt{16}\end{split}\)
\(\begin{split}{\small (3)}~3~,~-2.5~,~2.6~,~0~,~-\sqrt{16}\end{split}\)
\(\begin{split}{\small (4)}~\sqrt{7}~,~-\sqrt{13}\end{split}\)

p.52 問1\(\begin{split}{\small (1)}~\sqrt{15}\end{split}\)　　\(\begin{split}{\small (2)}~\sqrt{7}\end{split}\)　　\(\begin{split}{\small (3)}~\sqrt{3}\end{split}\)

p.52 問2\(\begin{split}{\small (1)}~\sqrt{8}\end{split}\)　　\(\begin{split}{\small (2)}~\sqrt{45}\end{split}\)
\(\begin{split}{\small (3)}~\sqrt{98}\end{split}\)　　\(\begin{split}{\small (4)}~\sqrt{75}\end{split}\)

p.53 問3\(\begin{split}{\small (1)}~2\sqrt{6}\end{split}\)　　\(\begin{split}{\small (2)}~2\sqrt{14}\end{split}\)
\(\begin{split}{\small (3)}~5\sqrt{3}\end{split}\)　　\(\begin{split}{\small (4)}~10\sqrt{2}\end{split}\)

p.53 問4

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\(\begin{split}{\small (1)}~\frac{\,\sqrt{2}\,}{\,3\,}\end{split}\)　　\(\begin{split}{\small (2)}~\frac{\,\sqrt{13}\,}{\,7\,}\end{split}\)

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\(\begin{split}{\small (3)}~\frac{\,\sqrt{11}\,}{\,10\,}\end{split}\)　　\(\begin{split}{\small (4)}~\frac{\,3\sqrt{3}\,}{\,10\,}\end{split}\)

p.54 問1\(\begin{split}{\small (1)}~3\sqrt{2}\end{split}\)　　\(\begin{split}{\small (2)}~32\sqrt{21}\end{split}\)
\(\begin{split}{\small (3)}~6\sqrt{10}\end{split}\)　　\(\begin{split}{\small (4)}~-15\sqrt{2}\end{split}\)
\(\begin{split}{\small (5)}~18\sqrt{2}\end{split}\)　　\(\begin{split}{\small (6)}~28\end{split}\)

p.55 問2\(\begin{split}{\small (1)}~5\sqrt{5}\end{split}\)　　\(\begin{split}{\small (2)}~9\sqrt{3}\end{split}\)
\(\begin{split}{\small (3)}~8\sqrt{6}\end{split}\)　　\(\begin{split}{\small (4)}~4\end{split}\)

p.55 問3

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\(\begin{split}{\small (1)}~\frac{\,\sqrt{5}\,}{\,5\,}\end{split}\)　　\(\begin{split}{\small (2)}~\frac{\,\sqrt{14}\,}{\,7\,}\end{split}\)

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\(\begin{split}{\small (3)}~\frac{\,\sqrt{15}\,}{\,6\,}\end{split}\)　　\(\begin{split}{\small (4)}~\frac{\,4\sqrt{2}\,}{\,3\,}\end{split}\)

p.55 問4

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\(\begin{split}{\small (1)}~\frac{\,\sqrt{10}\,}{\,5\,}\end{split}\)　　\(\begin{split}{\small (2)}~\frac{\,\sqrt{10}\,}{\,2\,}\end{split}\)

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\(\begin{split}{\small (3)}~\frac{\,3\sqrt{5}\,}{\,5\,}\end{split}\)　　\(\begin{split}{\small (4)}~\frac{\,2\sqrt{21}\,}{\,7\,}\end{split}\)

p.56 問1\(\begin{split}{\small (1)}~10\sqrt{6}\end{split}\)　　\(\begin{split}{\small (2)}~14\sqrt{7}\end{split}\)
\(\begin{split}{\small (3)}~\sqrt{2}\end{split}\)　　\(\begin{split}{\small (4)}~-3\sqrt{3}\end{split}\)
\(\begin{split}{\small (5)}~-2\sqrt{5}\end{split}\)　　\(\begin{split}{\small (6)}~\sqrt{10}\end{split}\)

p.57 問2１辺が \(\sqrt{2}+\sqrt{3}\) の正方形の面積は、図より、
　\(\sqrt{6}+3+2+\sqrt{6}=2\sqrt{6}+5\)
１辺が \(\sqrt{5}\) の正方形の面積は、
　\(\sqrt{5}{\, \small \times \,}\sqrt{5}=5\)
よって、 \(\sqrt{2}+\sqrt{3}\) は \(\sqrt{5}\) とならない

p.57 問3\(\begin{split}{\small (1)}~7\sqrt{2}+5\end{split}\)　　\(\begin{split}{\small (2)}~4\sqrt{7}-3\sqrt{6}\end{split}\)
\(\begin{split}{\small (3)}~5\sqrt{10}-2\sqrt{5}\end{split}\)　　\(\begin{split}{\small (4)}~2\sqrt{2}-\sqrt{3}\end{split}\)

p.57 問4\(\begin{split}{\small (1)}~3\sqrt{6}\end{split}\)　　\(\begin{split}{\small (2)}~\sqrt{7}\end{split}\)
\(\begin{split}{\small (3)}~-\sqrt{3}+7\sqrt{5}\end{split}\)　　\(\begin{split}{\small (4)}~\sqrt{10}-\sqrt{5}\end{split}\)

p.58 問1\(\begin{split}{\small (1)}~4\sqrt{15}+\sqrt{10}\end{split}\)　　\(\begin{split}{\small (2)}~18-9\sqrt{2}\end{split}\)
\(\begin{split}{\small (3)}~6+\sqrt{5}\end{split}\)　　\(\begin{split}{\small (4)}~9-\sqrt{6}\end{split}\)

p.58 問2\(\begin{split}{\small (1)}~-6-2\sqrt{2}\end{split}\)　　\(\begin{split}{\small (2)}~4+2\sqrt{3}\end{split}\)
\(\begin{split}{\small (3)}~2\end{split}\)　　\(\begin{split}{\small (4)}~14-6\sqrt{5}\end{split}\)

p.59 問3\(\begin{split}{\small (1)}~\sqrt{2}\end{split}\)　　\(\begin{split}{\small (2)}~2\sqrt{5}\end{split}\)

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\(\begin{split}{\small (3)}~\frac{\,7\sqrt{6}\,}{\,2\,}\end{split}\)　　\(\begin{split}{\small (4)}~\frac{\,8\sqrt{3}\,}{\,3\,}\end{split}\)

p.59 問4　\(a=5~,~20\) など

p.60 問1\(\begin{split}{\small (1)}~7\end{split}\)　　\(\begin{split}{\small (2)}~7-6\sqrt{7}\end{split}\)

p.60 問2\(\begin{split}{\small (1)}~17.32\end{split}\)　　\(\begin{split}{\small (2)}~54.77\end{split}\)
\(\begin{split}{\small (3)}~173.2\end{split}\)　　\(\begin{split}{\small (4)}~0.5477\end{split}\)
\(\begin{split}{\small (5)}~0.1732\end{split}\)　　\(\begin{split}{\small (6)}~0.05477\end{split}\)

p.61 問3　縦の長さ：横の長さ \(=\sqrt{2}\,:\,1\)

p.61 問4Ｂ５判は、
　縦の長さ：横の長さ \(=\sqrt{2}\,:\,1\)
Ｂ４判では、
　縦の長さ：横の長さ
\(\begin{split}~~=~&2\,:\,\sqrt{2}
\\[2pt]~~=~&2{\, \small \times \,}\sqrt{2}\,:\,\sqrt{2}{\, \small \times \,}\sqrt{2}
\\[2pt]~~=~&2\sqrt{2}\,:\,2
\\[2pt]~~=~&\sqrt{2}\,:\,1
\end{split}\)
よって、比が等しくなる

p.63 問1　\(23.5≦ a < 24.5\)
誤差の絶対値は最大で、\(0.5\)

p.63 問2　\(2.4\)

p.63 問3\(\begin{split}{\small (1)}~1.53{\, \small \times \,}10^2\end{split}\)　　\(\begin{split}{\small (2)}~7.85{\, \small \times \,}10^3\end{split}\)
\(\begin{split}{\small (3)}~2.70{\, \small \times \,}10^5\end{split}\)

p.64 基本の問題 1\(\begin{split}{\small (1)}~\sqrt{14}\end{split}\)　　\(\begin{split}{\small (2)}~\sqrt{48}\end{split}\)

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\(\begin{split}{\small (3)}~2\sqrt{13}\end{split}\)　　\(\begin{split}{\small (4)}~\frac{\,\sqrt{6}\,}{\,6\,}\end{split}\)

p.64 基本の問題 2\(\begin{split}{\small (1)}~6\sqrt{10}\end{split}\)　　\(\begin{split}{\small (2)}~98\end{split}\)
\(\begin{split}{\small (3)}~5\end{split}\)　　\(\begin{split}{\small (4)}~2\sqrt{3}\end{split}\)

p.64 基本の問題 3\(\begin{split}{\small (1)}~5\sqrt{6}\end{split}\)　　\(\begin{split}{\small (2)}~-5\sqrt{3}\end{split}\)
\(\begin{split}{\small (3)}~5\sqrt{5}+3\end{split}\)　　\(\begin{split}{\small (4)}~\sqrt{5}\end{split}\)

p.64 基本の問題 4\(\begin{split}{\small (1)}~6\sqrt{3}+\sqrt{6}\end{split}\)　　\(\begin{split}{\small (2)}~3-\sqrt{6}\end{split}\)
\(\begin{split}{\small (3)}~-14\end{split}\)　　\(\begin{split}{\small (4)}~-10-6\sqrt{2}\end{split}\)
\(\begin{split}{\small (5)}~3\sqrt{6}\end{split}\)　　\(\begin{split}{\small (6)}~2\sqrt{5}\end{split}\)

p.64 基本の問題 5\(\begin{split}{\small (1)}~3.15{\, \small \times \,}10^2~{\rm mL}\end{split}\)
\(\begin{split}{\small (2)}~6.80{\, \small \times \,}10^3~{\rm m}\end{split}\)

p.64 まちがえやすい問題\(\sqrt{8}+\sqrt{32}=\sqrt{8+32}\) と計算できない

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\(\begin{split}&\sqrt{8}+\sqrt{32}
\\[2pt]~~=~&2\sqrt{2}+4\sqrt{2}
\\[2pt]~~=~&6\sqrt{2}
\end{split}\)