啓林館：未来へ広がる数学３

p.40 問1\(\begin{split}{\small (1)}~5~,~-5\end{split}\)　　\(\begin{split}{\small (2)}~1~,~-1\end{split}\)
\(\begin{split}{\small (3)}~9~,~-9\end{split}\)　　\(\begin{split}{\small (4)}~7~,~-7\end{split}\)

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\(\begin{split}{\small (5)}~\frac{\,3\,}{\,4\,}~,~-\frac{\,3\,}{\,4\,}\end{split}\)　　\(\begin{split}{\small (6)}~\frac{\,1\,}{\,2\,}~,~-\frac{\,1\,}{\,2\,}\end{split}\)

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\(\begin{split}{\small (7)}~0.6~,~-0.6\end{split}\)　　\(\begin{split}{\small (8)}~0.3~,~-0.3\end{split}\)

p.41 問2\(\begin{split}{\small (1)}~\sqrt{7}~,~-\sqrt{7}\end{split}\)
\(\begin{split}{\small (2)}~\sqrt{0.3}~,~-\sqrt{0.3}\end{split}\)

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

p.41 問3\(\begin{split}~~~\left(\sqrt{5}\right)^2=5~~,~~\left(-\sqrt{5}\right)^2=5\end{split}\)

p.42 問4\(\begin{split}{\small (1)}~7\end{split}\)　　\(\begin{split}{\small (2)}~-8\end{split}\)

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\(\begin{split}{\small (3)}~0.5\end{split}\)　　\(\begin{split}{\small (4)}~-\frac{\,3\,}{\,4\,}\end{split}\)

p.42 問5\(\begin{split}{\small (1)}~\pm \sqrt{5}\end{split}\)　　\(\begin{split}{\small (2)}~\pm 0.3\end{split}\)

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\(\begin{split}{\small (3)}~\pm \sqrt{\frac{\,2\,}{\,7\,}}\end{split}\)　　\(\begin{split}{\small (4)}~\pm \frac{\,4\,}{\,9\,}\end{split}\)

p.43 問6\(\begin{split}{\small (1)}~3< \sqrt{10}\end{split}\)　　\(\begin{split}{\small (2)}~\sqrt{0.5}> 0.5\end{split}\)
\(\begin{split}{\small (3)}~-\sqrt{3}< -\sqrt{2}\end{split}\)　　\(\begin{split}{\small (4)}~-\sqrt{7}> -7\end{split}\)

p.43 練習問題1.\(\begin{split}{\small (1)}~\pm 3\end{split}\)　　\(\begin{split}{\small (2)}~\pm 20\end{split}\)
　\(\begin{split}{\small (3)}~\pm 0.8\end{split}\)　　\(\begin{split}{\small (4)}~\pm \frac{\,3\,}{\,7\,}\end{split}\)

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2.\(\begin{split}{\small (1)}~9\end{split}\)　　\(\begin{split}{\small (2)}~0.4\end{split}\)

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　\(\begin{split}{\small (3)}~-10\end{split}\)　　\(\begin{split}{\small (4)}~-\frac{\,2\,}{\,5\,}\end{split}\)

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3.\(\begin{split}~~~\left(\sqrt{6}\right)^2=6~~,~~\left(-\sqrt{6}\right)^2=6\end{split}\)

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4.\(\begin{split}~~~-\sqrt{5}< -\sqrt{2}< 0<\sqrt{3}<\sqrt{6}\end{split}\)

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5.\(\begin{split}~~~a=1~,~2~,~3\end{split}\)

p.44 問1\(\begin{split}~~~1.41^2=1.9881\end{split}\)
\(\begin{split}~~~1.42^2=2.0164\end{split}\)
\(\begin{split}~~~1.9881<\sqrt{2}<2.0164\end{split}\)
\(~~~\)小数第２位の数は \(1\)

p.45 問2\(\begin{split}~~~\sqrt{10}=3.162\end{split}\)
\(\begin{split}~~~\sqrt{15}=3.873\end{split}\)

p.45 問3\(\begin{split}~~~4.24~{\rm m}\end{split}\)

p.46 問1

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有理数は、\(\begin{split}0.1~,~-5~,~\sqrt{16}~,~\sqrt{\frac{\,4\,}{\,9\,}}\end{split}\)

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無理数は、\(\begin{split}-\sqrt{7}~,~-\sqrt{2}\end{split}\)

p.49 問1\(\begin{split}~~~1.55≦ a < 1.65\end{split}\)

p.49 問2\(\begin{split}{\small (1)}~1.21\times 10^3\end{split}\)
\(\begin{split}{\small (2)}~4.80\times 10^4\end{split}\)

p.51 問1

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\(\begin{split}&\left(\frac{\,\sqrt{2}\,}{\,\sqrt{3}\,}\right)^2
\\[3pt]~~=~&\frac{\,\sqrt{2}\,}{\,\sqrt{3}\,}\times \frac{\,\sqrt{2}\,}{\,\sqrt{3}\,}
\\[3pt]~~=~&\frac{\,\sqrt{2}\times\sqrt{2}\,}{\,\sqrt{3}\times\sqrt{3}\,}
\\[3pt]~~=~&\frac{\,2\,}{\,3\,}
\end{split}\)

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この式から \(\begin{split}{\frac{\,\sqrt{2}\,}{\,\sqrt{3}\,}}\end{split}\) は \(\begin{split}{\frac{\,2\,}{\,3\,}}\end{split}\) の平方根のうち正の方、つまり \(\begin{split}\sqrt{{\frac{\,2\,}{\,3\,}}}\end{split}\) に等しくなります

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p.52 問2\(\begin{split}{\small (1)}~\sqrt{30}\end{split}\)　　\(\begin{split}{\small (2)}~20\end{split}\)
\(\begin{split}{\small (3)}~-\sqrt{14}\end{split}\)　　\(\begin{split}{\small (4)}~\sqrt{13}\end{split}\)

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\(\begin{split}{\small (5)}~3\end{split}\)　　\(\begin{split}{\small (6)}~-\sqrt{\frac{\,7\,}{\,6\,}}\end{split}\)

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p.52 問3\(\begin{split}{\small (1)}~\sqrt{8}\end{split}\)　　\(\begin{split}{\small (2)}~\sqrt{27}\end{split}\)　　\(\begin{split}{\small (3)}~\sqrt{2}\end{split}\)

p.53 問4

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

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\(\begin{split}{\small (3)}~10\sqrt{3}\end{split}\)　　\(\begin{split}{\small (4)}~\frac{\,\sqrt{2}\,}{\,10\,}\end{split}\)

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p.53 問5\(\begin{split}{\small (1)}~3\sqrt{15}\end{split}\)　　\(\begin{split}{\small (2)}~14\sqrt{3}\end{split}\)

p.54 問6\(\begin{split}{\small (1)}~6\sqrt{6}\end{split}\)　　\(\begin{split}{\small (2)}~5\sqrt{6}\end{split}\)
\(\begin{split}{\small (3)}~16\sqrt{3}\end{split}\)　　\(\begin{split}{\small (4)}~6\sqrt{35}\end{split}\)

p.54 問7

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\(\begin{split}{\small (1)}~\frac{\,\sqrt{6}\,}{\,6\,}\end{split}\)　　\(\begin{split}{\small (2)}~\frac{\,\sqrt{15}\,}{\,5\,}\end{split}\)　　\(\begin{split}{\small (3)}~\frac{\,3\sqrt{2}\,}{\,2\,}\end{split}\)

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p.54 問8

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

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p.55 問9\(\begin{split}{\small (1)}~4.472\end{split}\)　　\(\begin{split}{\small (2)}~8.944\end{split}\)　　\(\begin{split}{\small (3)}~1.118\end{split}\)

p.55 話しあおう\(\begin{split}{\small (1)}~7.07\end{split}\)　　\(\begin{split}{\small (2)}~22.36\end{split}\)　　\(\begin{split}{\small (3)}~70.7\end{split}\)
\(\begin{split}{\small (4)}~0.707\end{split}\)　　\(\begin{split}{\small (5)}~0.2236\end{split}\)　　\(\begin{split}{\small (6)}~0.0707\end{split}\)

p.55 練習問題

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1.\(\begin{split}{\small (1)}~6\sqrt{2}\end{split}\)　　\(\begin{split}{\small (2)}~\frac{\,3\,}{\,2\,}\end{split}\)　　\(\begin{split}{\small (3)}~20\sqrt{6}\end{split}\)

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

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2.\(\begin{split}{\small (1)}~\frac{\,\sqrt{3}\,}{\,3\,}\end{split}\)　　\(\begin{split}{\small (2)}~\frac{\,\sqrt{21}\,}{\,7\,}\end{split}\)　　\(\begin{split}{\small (3)}~\frac{\,\sqrt{6}\,}{\,3\,}\end{split}\)

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

p.57 問2\(\begin{split}{\small (1)}~8\sqrt{3}\end{split}\)　　\(\begin{split}{\small (2)}~10\sqrt{2}\end{split}\)
\(\begin{split}{\small (3)}~0\end{split}\)　　\(\begin{split}{\small (4)}~-2\sqrt{5}\end{split}\)

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

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

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

p.58 問6\(\begin{split}{\small (1)}~3-2\sqrt{2}\end{split}\)　　\(\begin{split}{\small (2)}~-1\end{split}\)
\(\begin{split}{\small (3)}~23+9\sqrt{3}\end{split}\)　　\(\begin{split}{\small (4)}~-5-6\sqrt{2}\end{split}\)

p.58 練習問題1.\(\begin{split}{\small (1)}~7\sqrt{3}\end{split}\)　　\(\begin{split}{\small (2)}~4\sqrt{5}\end{split}\)
　\(\begin{split}{\small (3)}~-6\sqrt{6}-\sqrt{3}\end{split}\)　　\(\begin{split}{\small (4)}~\sqrt{7}\end{split}\)

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　\(\begin{split}{\small (5)}~\frac{\,3\sqrt{3}\,}{\,4\,}\end{split}\)　　\(\begin{split}{\small (6)}~-\frac{\,\sqrt{6}\,}{\,2\,}\end{split}\)

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　\(\begin{split}{\small (7)}~15-3\sqrt{5}\end{split}\)　　\(\begin{split}{\small (8)}~-5+2\sqrt{3}\end{split}\)
　\(\begin{split}{\small (9)}~5-2\sqrt{6}\end{split}\)　　\(\begin{split}{\small (10)}~6+2\sqrt{5}\end{split}\)
　\(\begin{split}{\small (11)}~4\end{split}\)　　\(\begin{split}{\small (12)}~5-3\sqrt{2}\end{split}\)

p.60 問1\(\begin{split}~~~200\pi ~{\rm cm}^2\end{split}\)

p.60 問2\(\begin{split}~~~14.1~{\rm cm}\end{split}\)

p.60 問3\(\begin{split}~~~17.3~{\rm cm}\end{split}\)

p.61 問4\(\begin{split}~~~14.1~{\rm cm}\end{split}\)

p.61 練習問題1.\(\begin{split}~~~4\sqrt{6}~{\rm cm}\end{split}\)

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2.\(\begin{split}{\small (1)}~5a-4b=30\end{split}\)
　\(\begin{split}{\small (2)}~5\sqrt{2}~{\rm cm}\end{split}\)

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　\(\begin{split}{\small (3)}~\frac{\,25\sqrt{2}-30\,}{\,4\,}~{\rm cm}\end{split}\)

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　\(\begin{split}{\small (4)}~1.3~{\rm cm}\end{split}\)