数研出版：これからの数学３

p.43 問1\(\begin{split}{\small (1)}~4~,~-4\end{split}\)　　\(\begin{split}{\small (2)}~7~,~-7\end{split}\)
\(\begin{split}{\small (3)}~1~,~-1\end{split}\)

p.43 問2

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\(\begin{split}{\small (1)}~\frac{\,5\,}{\,6\,}~,~-\frac{\,5\,}{\,6\,}\end{split}\)　　\(\begin{split}{\small (2)}~\frac{\,2\,}{\,9\,}~,~-\frac{\,2\,}{\,9\,}\end{split}\)

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\(\begin{split}{\small (3)}~0.2~,~-0.2\end{split}\)

p.44 問3\(\begin{split}~~~~1.41^2=1.9881\end{split}\)
\(\begin{split}~~~~1.42^2=2.0164\end{split}\)
よって、\(x\) は \(1.41\) より大きく \(1.42\) より小さい
\(\begin{split}~~~~1.41< x < 1.42\end{split}\)
したがって、\(x\) の値の小数第２位の数は \(1\) となる

p.45 問4\(\begin{split}{\small (1)}~\pm\sqrt{3}\end{split}\)　　\(\begin{split}{\small (2)}~\pm\sqrt{15}\end{split}\)
\(\begin{split}{\small (3)}~\pm\sqrt{0.7}\end{split}\)　　\(\begin{split}{\small (4)}~\pm\sqrt{\frac{\,5\,}{\,6\,}}\end{split}\)

p.45 問5\(\begin{split}~~~\sqrt{2}≒1.414\end{split}\)

p.46 問6\(\begin{split}{\small (1)}~7\end{split}\)　　\(\begin{split}{\small (2)}~6\end{split}\)
\(\begin{split}{\small (3)}~-2\end{split}\)　　\(\begin{split}{\small (4)}~-5\end{split}\)

p.47 問7

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\(\begin{split}{\small (1)}~3\end{split}\)　　\(\begin{split}{\small (2)}~-8\end{split}\)　　\(\begin{split}{\small (3)}~\frac{\,3\,}{\,4\,}\end{split}\)

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\(\begin{split}{\small (4)}~-0.4\end{split}\)　　\(\begin{split}{\small (5)}~12\end{split}\)　　\(\begin{split}{\small (6)}~17\end{split}\)

p.47 問8\({\small (1)}~\sqrt{25}=5\) である
\({\small (2)}~9\) の平方根は \(\pm3\) である

p.48 問9\(\begin{split}{\small (1)}~\sqrt{2}<\sqrt{5}\end{split}\)
\(\begin{split}{\small (2)}~\sqrt{10}>3\end{split}\)
\(\begin{split}{\small (3)}~-\sqrt{6}>-\sqrt{7}\end{split}\)
\(\begin{split}{\small (4)}~-6<-\sqrt{35}\end{split}\)

p.48 問10\(\begin{split}{\small (1)}~\sqrt{5}<5\end{split}\)
\(\begin{split}{\small (2)}~\sqrt{0.5}>0.5\end{split}\)

p.49 問1

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\(\begin{split}{\small (1)}~\frac{\,2\,}{\,5\,}\end{split}\)　　\(\begin{split}{\small (2)}~\frac{\,1\,}{\,8\,}\end{split}\)　　\(\begin{split}{\small (3)}~\frac{\,52\,}{\,25\,}\end{split}\)

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p.50 問2

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有理数は、\(\begin{split}\frac{\,6\,}{\,5\,}~,~\sqrt{4}~,~-\sqrt{\frac{\,9\,}{\,4\,}}\end{split}\)

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無理数は、\(\begin{split}\sqrt{6}\end{split}\)

p.55 問1\(\begin{split}{\small (1)}~\sqrt{14}\end{split}\)　　\(\begin{split}{\small (2)}~6\end{split}\)
\(\begin{split}{\small (3)}~\sqrt{3}\end{split}\)　　\(\begin{split}{\small (4)}~\sqrt{13}\end{split}\)

p.55 問2\(\begin{split}{\small (1)}~\sqrt{7}\end{split}\)　　\(\begin{split}{\small (2)}~4\end{split}\)

p.55 問3\(\begin{split}{\small (1)}~\sqrt{18}\end{split}\)　　\(\begin{split}{\small (2)}~\sqrt{80}\end{split}\)　　\(\begin{split}{\small (3)}~\sqrt{7}\end{split}\)

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

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

p.56 問6

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\(\begin{split}{\small (1)}~\frac{\,\sqrt{2}\,}{\,5\,}\end{split}\)　　\(\begin{split}{\small (2)}~\frac{\,\sqrt{5}\,}{\,9\,}\end{split}\)

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\(\begin{split}{\small (3)}~\frac{\,\sqrt{3}\,}{\,10\,}\end{split}\)　　\(\begin{split}{\small (4)}~\frac{\,\sqrt{11}\,}{\,100\,}\end{split}\)

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p.57 問7\(\begin{split}{\small (1)}~4\sqrt{3}\end{split}\)　　\(\begin{split}{\small (2)}~7\sqrt{6}\end{split}\)
\(\begin{split}{\small (3)}~30\end{split}\)　　\(\begin{split}{\small (4)}~8\sqrt{35}\end{split}\)
\(\begin{split}{\small (5)}~15\sqrt{7}\end{split}\)　　\(\begin{split}{\small (6)}~24\sqrt{15}\end{split}\)

p.58 問8

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\(\begin{split}{\small (1)}~\frac{\,3\sqrt{5}\,}{\,5\,}\end{split}\)　　\(\begin{split}{\small (2)}~\frac{\,\sqrt{30}\,}{\,3\,}\end{split}\)

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

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p.58 問9

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\(\begin{split}{\small (1)}~\frac{\,\sqrt{6}\,}{\,2\,}\end{split}\)　　\(\begin{split}{\small (2)}~\frac{\,2\sqrt{15}\,}{\,3\,}\end{split}\)　　\(\begin{split}{\small (3)}~\frac{\,\sqrt{21}\,}{\,3\,}\end{split}\)

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p.59 問1\(\begin{split}{\small (1)}~11\sqrt{2}\end{split}\)　　\(\begin{split}{\small (2)}~2\sqrt{5}\end{split}\)
\(\begin{split}{\small (3)}~-\sqrt{3}\end{split}\)　　\(\begin{split}{\small (4)}~0\end{split}\)

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

p.60 問3\(\begin{split}{\small (1)}~9\sqrt{2}\end{split}\)　　\(\begin{split}{\small (2)}~2\sqrt{3}\end{split}\)
\(\begin{split}{\small (3)}~-\sqrt{2}\end{split}\)　　\(\begin{split}{\small (4)}~-5\sqrt{5}\end{split}\)
\(\begin{split}{\small (5)}~2\sqrt{3}+\sqrt{2}\end{split}\)　　\(\begin{split}{\small (6)}~3\sqrt{2}+\sqrt{3}\end{split}\)

p.60 問4\(\begin{split}{\small (1)}~7\sqrt{5}\end{split}\)　　\(\begin{split}{\small (2)}~2\sqrt{3}\end{split}\)

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

p.61 問1\(\begin{split}{\small (1)}~\sqrt{6}+2\end{split}\)
\(\begin{split}{\small (2)}~6\sqrt{6}-6\sqrt{3}\end{split}\)
\(\begin{split}{\small (3)}~6+3\sqrt{6}\end{split}\)
\(\begin{split}{\small (4)}~\sqrt{3}-3\end{split}\)
\(\begin{split}{\small (5)}~3\sqrt{2}+2\sqrt{3}+\sqrt{6}+2\end{split}\)
\(\begin{split}{\small (6)}~2\sqrt{2}+\sqrt{5}\end{split}\)

p.62 問2\(\begin{split}{\small (1)}~5+4\sqrt{2}\end{split}\)　　\(\begin{split}{\small (2)}~4+2\sqrt{3}\end{split}\)
\(\begin{split}{\small (3)}~7-2\sqrt{10}\end{split}\)　　\(\begin{split}{\small (4)}~5\end{split}\)
\(\begin{split}{\small (5)}~30-12\sqrt{6}\end{split}\)　　\(\begin{split}{\small (6)}~2\end{split}\)

p.62 問3\(\begin{split}{\small (1)}~3\end{split}\)　　\(\begin{split}{\small (2)}~4\sqrt{10}\end{split}\)　　\(\begin{split}{\small (3)}~10+2\sqrt{10}\end{split}\)

p.64 問1\(\begin{split}{\small (1)}~17.32\end{split}\)　　\(\begin{split}{\small (2)}~54.77\end{split}\)
\(\begin{split}{\small (3)}~0.1732\end{split}\)　　\(\begin{split}{\small (4)}~0.5477\end{split}\)

p.64 問2\(\begin{split}{\small (1)}~2.828\end{split}\)　　\(\begin{split}{\small (2)}~5.656\end{split}\)
\(\begin{split}{\small (3)}~44.72\end{split}\)　　\(\begin{split}{\small (4)}~0.2236\end{split}\)

p.65 問3\(\begin{split}~~~~23.5 ≦ a < 24.5\end{split}\)

p.66 問4\(\begin{split}{\small (1)}~1~,~2\end{split}\)　　\(\begin{split}{\small (2)}~1~,~2~,~0\end{split}\)

p.66 問5\(\begin{split}{\small (1)}~6.24\times10^3\end{split}\)　　\(\begin{split}{\small (2)}~1.600\times10^5\end{split}\)

p.67 問6\(\begin{eqnarray}~{\rm AB}&=&\sqrt{2}
\\[2pt]~~~{\rm AD}&=&1+1=2
\end{eqnarray}\)
であるので、たてとよこの比は、
\(\begin{split}~~~~~~\sqrt{2}~:~2\end{split}\)
\(\sqrt{2}\) をかけると、
\(\begin{split}~~=~&\sqrt{2}\times\sqrt{2}~:~2\times\sqrt{2}
\\[2pt]~~=~&2~:~2\sqrt{2}
\end{split}\)
\(2\) でわると、
\(\begin{split}~~=~&1~:~\sqrt{2}
\end{split}\)
よって、Ｂ４判の紙の２辺の長さの比も \(1~:~\sqrt{2}\) となる