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%%
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%% white �� black�@�̒u������������Ɩ͔͉𓚗p�����ł��܂��B
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\begin{document}
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    \Large\bf $3$�N~������
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    \underline{\hspace{1cm}}�N\underline{\hspace{1cm}}�g\underline{\hspace{1cm}}��
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\begin{enumerate}

\item \fbox{�@�@�@} �ɂ��Ă͂܂錾�t�܂��͐��������Ȃ����B

\begin{enumerate}
\item ���鐔$x$��$2$�悷���$a$�ɂȂ�Ƃ��C$x$��$a$�� \fbox{�@\ajMaru{1}�@} �Ƃ����B�Ⴆ��$9$�� \fbox{�@\ajMaru{1}�@} �� \fbox{�@\ajMaru{2}�@} �ƂȂ�C$12$�� \fbox{�@\ajMaru{1}�@} �� \fbox{�@\ajMaru{3}�@} �ł���B

\item $m$�𐮐��C$n$��$0$�łȂ������Ƃ���Ƃ��C$\dfrac{\,m\,}{n}$�̂悤�ɁC�����ŕ\�����Ƃ��ł��鐔�� \fbox{�@\ajMaru{4}�@} �Ƃ����B
�Ⴆ�΁C$3$�� \fbox{�@\ajMaru{5}�@}�C0.25�� \fbox{�@\ajMaru{6}�@} �ƕ\�����Ƃ��ł���̂� \fbox{�@\ajMaru{4}�@} �ł���B
����ɑ΂���$\sqrt{\,2\,}$��$\sqrt{\,3\,}$�Ȃǂ̕����ł͕\�����Ƃ��ł��Ȃ����� \fbox{�@\ajMaru{7}�@} �Ƃ����B������$\sqrt{\,2\,}$�͏����ŕ\���� \fbox{�@\ajMaru{8}�@} �ƂȂ鐔�ł���B
(\ajMaru{8}�̌����͓��ɒ�߂Ȃ��C������\���Ă���ΉƂ���B)
\end{enumerate}

\begin{tabular}{|@{\vrule width 0.4pt}c@{}|c|@{}c@{}|c|@{\vrule width 0.4pt}}
\noalign{\hrule height 0.4pt}\hline
& \hspace{33mm} & & \hspace{33mm} \\[-8pt]
~\ajMaru{1}~ & \color{white}{������} & ~\ajMaru{2}~ & \color{white}{$\pm\,3$} \\[-8pt]
& & & \\
\hline
& & & \\[-8pt]
~\ajMaru{3}~ & {\color{white}{$\pm\,2\sqrt{\,3\,}$}} & ~\ajMaru{4}~ & \color{white}{�L����} \\[-8pt]
& & & \\
\hline
& & & \\[-8pt]
~\ajMaru{5}~ & {\color{white}{$\dfrac{\,3\,}{1}$}} & ~\ajMaru{6}~ & \color{white}{$\dfrac{1}{\,4\,}$} \\[-8pt]
& & & \\
\hline
& & & \\[-8pt]
~\ajMaru{7}~ & {\color{white}{������}} & ~\ajMaru{8}~ & \color{white}{$1.41421356\cdots$} \\[-8pt]
& & & \\
\noalign{\hrule height 0.4pt}\hline
\end{tabular}

\item ���̌v�Z�����Ȃ����B
\begin{enumerate}
\item $\sqrt{\,2\,}\times\sqrt{\,32\,}$

\vspace{-2mm}
\LINEK{8}

\item $5\sqrt{\,7\,}+3\sqrt{\,7\,}$

\vspace{-2mm}
\LINEK{8\sqrt{\,7\,}}

\item $\sqrt{\,12\,}-\sqrt{\,75\,}$

{\color{white}{$=2\sqrt{\,3\,}-5\sqrt{\,3\,}$}}

\vspace{-2mm}
\LINEK{-3\sqrt{\,3\,}}

\item $7\div\sqrt{\,28\,}$

{\color{white}{$=\dfrac{7}{\,\sqrt{\,28\,}\,}\times\dfrac{\sqrt{\,28\,}}{\sqrt{\,28\,}}=\dfrac{7\times 2\sqrt{\,7\,}}{28}$}}

\vspace{-2mm}
\LINEK{\dfrac{\sqrt{\,7\,}}{2}}

\item $\sqrt{\,48\,}-2\sqrt{\,8\,}+5\sqrt{\,27\,}-\sqrt{\,50\,}$

{\color{white}{$=4\sqrt{\,3\,}-4\sqrt{\,2\,}+15\sqrt{\,3\,}-5\sqrt{\,2\,}$}}

\vspace{-2mm}
\LINEK{19\sqrt{\,3\,}-9\sqrt{\,2\,}}

\item $(5\sqrt{\,2\,}-4\sqrt{\,3\,})^2$

{\color{white}{$=(5\sqrt{\,2\,})^2-2\times5\sqrt{\,2\,}\times4\sqrt{\,3\,}+(4\sqrt{\,3\,})^2$}}

{\color{white}{$=50-40\sqrt{\,6\,}+48$}}

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\LINEK{98-40\sqrt{\,6\,}}

\end{enumerate}

\newpage

\item ����4�̐������������ɕs������p���đ召�֌W��\���Ȃ����B

$\dfrac{2}{\,7\,}\hspace{5mm}\dfrac{2}{\sqrt{\,7\,}}\hspace{5mm}\dfrac{\sqrt{\,2\,}}{7}\hspace{5mm}\sqrt{\,\dfrac{2}{\,7\,}\,}$

���l������

{\color{white}{$\dfrac{\sqrt{\,4\,}}{7}\hspace{2mm}\dfrac{\sqrt{\,28\,}}{7}\hspace{2mm}\dfrac{\sqrt{\,2\,}}{7}\hspace{2mm}\dfrac{\sqrt{\,14\,}}{7}$}}


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\LINEK{\dfrac{\sqrt{\,2\,}}{7}<\dfrac{2}{\,7\,}<\sqrt{\,\dfrac{2}{\,7\,}\,}<\dfrac{2}{\sqrt{\,7\,}}}

\item $\sqrt{\,20\,}=4.472$�Ƃ��Ď��̐��̋ߎ��l�����߂Ȃ����B

\begin{enumerate}
\item $\sqrt{\,80\,}$

{\color{white}{$\sqrt{\,80\,}=2\sqrt{\,20\,}=2\times 4.472$}}

\vspace{-5mm}
\LINEK{8.944}

\item $\dfrac{1}{\,\sqrt{2000}\,}$

\vspace{2mm}
{\color{white}{$\dfrac{\sqrt{\,2000\,}}{2000}=\dfrac{\sqrt{\,20\,}}{200}=4.472\div 200$}}

\vspace{-5mm}
\LINEK{0.02236}

\end{enumerate}

\item �����I\!��\!��\!�s\!�b\!�N��\!\,$2020$\!\,�N�ɗ\�肳��Ă��܂�\!�B\!$2020$\!\,���g�����ȉ��̎��������ɂȂ�ŏ��̎��R��$n$�����߂Ȃ����B

\begin{enumerate}
\item $\sqrt{\,2020\times n\,}$

{\color{white}{$2020=2^2\times 5\times 101$}}

\vspace{-5mm}
\LINEK{n=505}

\item $\sqrt{\,2020+ n\,}$

{\color{white}{$44^2=1936\,,\,45^2=2025$}}

\vspace{-5mm}
\LINEK{n=5}

\item $\sqrt{\,2020- n\,}$

\vspace{-5mm}
\LINEK{n=84}

\end{enumerate}

\item �}�͒�ʂ̔��a��$\sqrt{\,3\,}$ \ajLig{cm}�C������$\sqrt{\,2\,}$ \ajLig{cm}�C����̒�����$\sqrt{\,5\,}$ \ajLig{cm}�̉~���ł���B���̂��Ƃɂ��Ĉȉ��̖₢�ɓ����Ȃ����B�������~������$\pi$�Ƃ���B

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\begin{enumerate}
\item �\�ʐς����߂Ȃ����B

{\color{white}{\begin{tabular}{@{}r@{}c@{}l@{}}
$S_1$ & $\,=\,$ & $\pi\times (\sqrt{3})^2=3\pi$ \\
$S_2$ & $\,=\,$ & $2\times\pi\times\sqrt{3}\times\sqrt{5}\times\dfrac{1}{\,2\,}$ \\
      & $\,=\,$ & $\sqrt{15}\,\pi$ \\
\end{tabular}}}

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\item �̐ς����߂Ȃ����B

{\color{white}{$V=\dfrac{1}{\,3\,}\times \pi\times (\sqrt{3})^2\times\sqrt{2}$}}

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\underline{���@\hspace{20mm}{\color{white}{$\sqrt{2}\,\pi$~~}}\hspace*{5mm}\ajLig{cm3}\hspace*{5mm}}
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\end{enumerate}

\end{enumerate}
\end{document}
