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%%
%% �������@�������當�����͂��܂�܂��@������
%%
%% white �� black�@�̒u������������Ɩ͔͉𓚗p�����ł��܂��B
%%
%%
\begin{document}
\twocolumn[%
  \begin{center}
    \Large\bf ���w��~$3$�N~������
  \end{center}
  \begin{flushright}
    \underline{\hspace{1cm}}�N\underline{\hspace{1cm}}�g\underline{\hspace{1cm}}��
    \hspace{1zw}����\underline{\hspace{5cm}}
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 \vspace{5mm}]

\parindent = 0zw 
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\begin{enumerate}

\item �ȉ��̕\�͐��𕪗ނ������̂ł���B�ȉ��̖₢�ɓ����Ȃ����B

\vspace{10mm}
\hspace{-5mm}
$��\left\{
\begin{array}{@{\,}ll}
  \fbox{~~(�A)~~} \\
\\
\\
  \fbox{~~(�C)~~}\,\,\,\,�c�c�c�c�c�c�c�c�c�z���Ȃ�\,\fbox{~~(�G)~~}�c
\end{array}
\right. $

\vspace{-31mm}
\hspace{15mm}
$\left\{
\begin{array}{@{\,}ll}
  ���� \\
\\[-6pt]
\\
  \fbox{~~(�E)~~}\,(�����ȊO�̗L����)
\end{array}
\right. 
$

\vspace{-26.5mm}
\hspace{27mm}
$\left\{
\begin{array}{@{\,}ll}
  ���̐���(���R��) �c�c�c�c�c�c�c\\
$0$~�c�c�c�c�c�c�c�c�c�c�c�c�c�c\\
  ���̐����c�c�c�c�c�c�c�c�c�c�c
\end{array}
\right. 
$

%\vspace{-1mm}
\hspace{60.5mm}
$\left\{
\begin{array}{@{\,}ll}
  �L�������c \\
  �z�����c
\end{array}
\right. 
$

\vspace{-28mm}\hspace{82mm}\ajMaru{1}

\hspace{82mm}\ajMaru{2}

\hspace{82mm}\ajMaru{3}

\vspace{0.5mm}
\hspace{82mm}\ajMaru{4}

\hspace{82mm}\ajMaru{5}

\vspace{1mm}
\hspace{82mm}\ajMaru{6}

\vspace{3mm}
\begin{enumerate}
\item �󗓂ɂ��Ă͂܂錾�t�������Ȃ����B

\vspace{1mm}
\hspace{-8mm}
\begin{tabular}{|@{\vrule width 0.4pt}c@{}|c|@{}c@{}|c|@{\vrule width 0.4pt}}
\noalign{\hrule height 0.4pt}\hline
& \hspace{30mm} & & \hspace{30mm} \\[-8pt]
~(�A)~ & \color{white}{�L����} & ~(�C)~ &  \color{white}{������} \\[-8pt]
& & & \\
\hline
& & & \\[-8pt]
~(�E)~ & \color{white}{����} & ~(�G)~ & \color{white}{��������} \\[-8pt]
& & & \\
\noalign{\hrule height 0.4pt}\hline
\end{tabular}

\vspace{1mm}
\item �ȉ��̐���\ajMaru{1}�`\ajMaru{6}�̂ǂ�ɂ��Ă͂܂�܂����C�ԍ��œ����Ȃ����B

\vspace{0.5mm}
\begin{tabular}{@{}|@{\vrule width 0.4pt}c@{}|@{}c@{}|@{}c@{}|@{}c@{}|@{}c@{}|@{\vrule width 0.4pt}}
\noalign{\hrule height 0.4pt}\hline
\hspace{14mm} & \hspace{14mm} & \hspace{14mm} & \hspace{14mm} & \hspace{14mm} \\[-12pt]
\,$\dfrac{\,12\,}{7}$\, & \,$-0.09$\, & \,$\sqrt{\,6\,}$\, & \,$\sqrt{\,25\,}$\, & \,$\sqrt{\,\dfrac{9}{\,4\,}\,}$\, \\[-12pt]
& & & & \\
\hline
 & & & & \\[-6pt]
\color{white}{\ajMaru{5}} & \color{white}{\ajMaru{4}} & \color{white}{\ajMaru{6}} & \color{white}{\ajMaru{1}} & \color{white}{\ajMaru{4}} \\[-6pt]
 & & & & \\
\noalign{\hrule height 0.4pt}\hline
\end{tabular}

\end{enumerate}

%%�������̌v�Z
\vspace{1mm}
\item ���̐��̕����������߂Ȃ����B

~(1)~$9$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)~$12$

\vspace{1mm}
%\hspace{-8mm}
\begin{tabular}{|@{\vrule width 0.4pt}c@{}|c|@{}c@{}|c|@{\vrule width 0.4pt}}
\noalign{\hrule height 0.4pt}\hline
& \hspace{30mm} & & \hspace{30mm} \\[-8pt]
~(1)~ & \color{white}{$\pm 3$} & ~(2)~ &  \color{white}{$\pm 2\sqrt{\,3\,}$} \\[-8pt]
& & & \\
\noalign{\hrule height 0.4pt}\hline
\end{tabular}

\vspace{1mm}
\item ���̎����v�Z���Ȃ����B

\begin{enumerate}

\item $5\sqrt{\,2\,} \times 2\sqrt{\,7\,}$

\vfill
\LINEK{10\sqrt{\,14\,}}

\item $3\sqrt{\,3\,}-4\sqrt{\,3\,}$

\vfill
\LINEK{-\sqrt{\,3\,}}

\item $2\sqrt{\,18\,}+\sqrt{\,12\,}-\sqrt{\,8\,}$

\hspace{-10mm}���v�Z��

\vfill
\LINEK{4\sqrt{\,2\,}+2\sqrt{\,3\,}}

\hspace{-10mm}���v�Z��

\item $\sqrt{\,3\,}(\sqrt{\,8\,}+\sqrt{\,3\,})-\dfrac{\,18\,}{\,\sqrt{\,6\,}\,}$

{\color{white}{$=2\sqrt{\,6\,}+3-3\sqrt{\,6\,}$}}

\vfill
\LINEK{3-\sqrt{\,6\,}}

\item $\dfrac{\,\sqrt{\,10\,}\,}{6}\div \dfrac{\,1\,}{\sqrt{\,54\,}}\times \dfrac{\,2\,}{\,\sqrt{\,5\,}\,}$

\hspace{-10mm}���v�Z��

{\color{white}{$=\dfrac{\,\sqrt{\,10\,}\,}{6}\times 3\sqrt{\,6\,}\times \dfrac{\,2\,}{\,\sqrt{\,5\,}\,}$}}

\vfill
\vfill
\LINEK{2\sqrt{\,3\,}}

\item $3\sqrt{\,6\,}\times \sqrt{\,2\,}-\dfrac{\,15\,}{\,\sqrt{\,3\,}\,}$

\hspace{-10mm}���v�Z��

{\color{white}{$=6\sqrt{\,3\,}-5\sqrt{\,3\,}$}}

\vfill
\vfill
\LINEK{\,\sqrt{\,3\,}}

\item $(2\sqrt{\,3\,}-1)(2\sqrt{\,3\,}+4)$

\hspace{-10mm}���v�Z��

{\color{white}{$=12+3\sqrt{\,3\,}-4$}}

\vfill
\vfill
\LINEK{8+3\sqrt{\,3\,}}

\end{enumerate}

\item ���̖₢�ɓ����Ȃ����B

%%�������̈Ӗ��̉��p
\begin{enumerate}
\item $3<\sqrt{\,x\,}\leqq 4$�ƂȂ�悤�Ȏ��R��$x$�����߂Ȃ����B

\hspace{-5mm}���l������
{\color{white}{$3^2<(\sqrt{\,x\,})^2\leqq 4^2$}}

{\color{white}{$9<x\leqq 16$}}

\vfill
\LINEK{10,\,11,\,12,\,13,\,14,\,15,\,16}


%%�ߎ��l�v�Z
\item $a=6+\sqrt{\,2\,}$\,,\,$b=6-\sqrt{\,2\,}$�̂Ƃ�$a^2-2ab+b^2$�̎��̒l�����߂Ȃ����B

\hspace{-10mm}���l������

{\color{white}{
\begin{tabular}{@{}r@{}c@{}l@{}}
$a^2-2ab+b^2$ & $=$ & $(a-b)^2$ \\
              & $=$ & $(6+\sqrt{\,2\,}-6+\sqrt{\,2\,})^2$ \\
              & $=$ & $(2\sqrt{\,2\,})^2$ \\
\end{tabular}
}}

\LINEK{8}

\item $\sqrt{\,24n\,}$�����R���ƂȂ鎩�R��$n$������������3���߂Ȃ����B

\hspace{-10mm}���l������

{\color{white}{$\sqrt{\,24n\,}=2\sqrt{\,6n\,}$���}}

{\color{white}{$6\times 1^2=6~,~6\times 2^2=24~,~6\times 3^2=54$}}

\vfill
\LINEK{6,24,54}

\end{enumerate}

\item �����̂������ɂ����Ă�$\sqrt{\,a\,}\times\sqrt{\,b\,}=\sqrt{\,a\times b\,}$�����藧���܂��B
���̂��Ƃ�$\sqrt{\,2\,}\times \sqrt{\,5\,}$���ɂ���$\sqrt{\,10\,}$�ɂȂ邱�Ƃ�������Ȃ����B

\vspace{1mm}
\hspace{-8mm}
\begin{tabular}{|@{\vrule width 0.3pt \hspace{2,5mm}}l|@{\vrule width 0.3pt}}
\noalign{\hrule height 0.3pt}\hline
�������� \\
{\color{white}{$x=\sqrt{\,2\,}\times\sqrt{\,5\,}$�Ƃ���}} \\
{\color{white}{$x^2=(\sqrt{\,2\,}\times\sqrt{\,5\,})^2$}}\\
{\color{white}{$x^2=(\sqrt{\,2\,}\times\sqrt{\,5\,})\times (\sqrt{\,2\,}\times\sqrt{\,5\,})$}}\\
{\color{white}{$x^2=(\sqrt{\,2\,})^2\times(\sqrt{\,5\,})^2$}}\\
{\color{white}{$x^2=2\times 5$}}\\
{\color{white}{$x^2=10$}}\\
{\color{white}{������������$x=\pm\sqrt{\,10\,}$}}\\
{\color{white}{$x>0$���$x=\sqrt{\,10\,}$}}\\
{\color{white}{�����$\sqrt{\,2\,}\times \sqrt{\,5\,}=\sqrt{\,10\,}$}}\\
~\hspace{85mm}~ \\
\noalign{\hrule height 0.3pt}\hline
\end{tabular}

\vspace{1mm}
\item $\sqrt{\,72\,}$��$2\sqrt{\,18\,}$\,,\,$3\sqrt{\,8\,}$\,,\,$6\sqrt{\,2\,}$�ƕ\�����Ƃ��ł��C���Ƃ̌`���܂߂��$4$�̈قȂ�`�œ�������\�����Ƃ��ł��܂��B$\sqrt{\,2016\,}$�͌��̌`���܂߂ĉ��ʂ�̕\�������ł��܂����B

\hspace{-8mm}
\begin{tabular}{|@{\vrule width 0.3pt \hspace{2,5mm}}l|@{\vrule width 0.3pt}}
\noalign{\hrule height 0.3pt}\hline
������������ѓ��� \\
{\color{white}{$2016=2^5\times 3^2\times 7$}} \\
{\color{white}{�������̈�����$4$,\,$9$,\,$16$,\,$36$,\,$144$�ł���B}}\\
{\color{white}{
\begin{tabular}{cl}
$4$�̂Ƃ� & $=2\sqrt{\,504\,}$ \\
$9$�̂Ƃ� & $=3\sqrt{\,224\,}$ \\
$16$�̂Ƃ� & $=4\sqrt{\,126\,}$ \\
$36$�̂Ƃ� & $=6\sqrt{\,56\,}$ \\
$144$�̂Ƃ� & $=12\sqrt{\,14\,}$ \\
\end{tabular}
}}\\
\multicolumn{1}{@{}|@{\vrule width 0.3pt}r@{}|@{\vrule width 0.3pt}}{\underline{~~~~~~{\color{white}{\,6\,}}~~~�ʂ�~~~}~~} \\[-12pt]
~\hspace{85mm}~ \\
\noalign{\hrule height 0.3pt}\hline
\end{tabular}

\end{enumerate}
\end{document}
