جواب کاردرکلاس صفحه 26 درس 2 ریاضی هشتم (عددهای اول)

\(\begin{array}{l}\sqrt {97} \simeq 9 \to \\\\\\\begin{array}{*{20}{c}}{}\\{97}\\\begin{array}{l}\underline {\,\,\,\,96\,\,\,\,\,} \\\,\,\,\,\,\,1\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,2\,\,\,} }\\{48}\end{array}} \right.}\\{}\end{array}\,\,\,\,\,\,\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{}\\{97}\\\begin{array}{l}\underline {\,\,\,\,96\,\,\,\,\,} \\\,\,\,\,\,\,1\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,3\,\,\,} }\\{32}\end{array}} \right.}\\{}\end{array}\,\,\,\,\,\,\,\,\,\,\,\,\,\\\\\\\begin{array}{*{20}{c}}{}\\{97}\\\begin{array}{l}\underline {\,\,\,\,95\,\,\,\,\,} \\\,\,\,\,\,\,2\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,5\,\,\,} }\\{19}\end{array}} \right.}\\{}\end{array}\,\,\,\,\,\,\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{}\\{97}\\\begin{array}{l}\underline {\,\,\,\,91\,\,\,\,\,} \\\,\,\,\,\,6\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,7\,\,\,} }\\{13}\end{array}} \right.}\\{}\end{array}\end{array}\)

\(\sqrt {131} \simeq 11 \to \)

پس باید آن را به عددهای اول 2، 3، 5، 7 و 11 تقسیم کنیم.

\(\begin{array}{l}\begin{array}{*{20}{c}}{}\\{131}\\\begin{array}{l}\underline {\,\,\,\,130\,\,\,\,\,} \\\,\,\,\,\,\,\,1\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,2\,\,\,} }\\{65}\end{array}} \right.}\\{}\end{array}\,\,\,\,\,\,\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{}\\{131}\\\begin{array}{l}\underline {\,\,\,\,129\,\,\,\,\,} \\\,\,\,\,\,\,2\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,3\,\,\,} }\\{43}\end{array}} \right.}\\{}\end{array}\,\,\,\,\,\,\,\,\,\,\,\,\,\\\\\\\begin{array}{*{20}{c}}{}\\{131}\\\begin{array}{l}\underline {\,\,\,\,\,130\,\,\,\,} \\\,\,\,\,\,\,\,1\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,5\,\,\,} }\\{26}\end{array}} \right.}\\{}\end{array}\,\,\,\,\,\,\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{}\\{131}\\\begin{array}{l}\underline {\,\,\,\,126\,\,\,\,\,} \\\,\,\,\,\,\,\,5\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,7\,\,\,} }\\{18}\end{array}} \right.}\\{}\end{array}\\\\\begin{array}{*{20}{c}}{}\\{131}\\\begin{array}{l}\underline {\,\,\,\,121\,\,\,\,\,} \\\,\,\,\,10\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,11\,\,\,} }\\{11}\end{array}} \right.}\\{}\end{array}\end{array}\)

چون تمام تقسیم ها باقیمانده دارند، 131 مضرب هیچ کدام نیست؛ یعنی عدد اول است.

\(\sqrt {143} \simeq 11 \to \)

پس باید آن را به عددهای اول 2، 3، 5، 7 و 11 تقسیم کنیم.

\(\begin{array}{l}\begin{array}{*{20}{c}}{}\\{143}\\\begin{array}{l}\underline {\,\,\,\,142\,\,\,\,\,} \\\,\,\,\,1\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,2\,\,\,} }\\{71}\end{array}} \right.}\\{}\end{array}\,\,\,\,\,\,\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{}\\{143}\\\begin{array}{l}\underline {\,\,\,141\,\,\,\,\,} \\\,\,\,\,2\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,3\,\,\,} }\\{47}\end{array}} \right.}\\{}\end{array}\,\,\,\,\,\,\,\,\,\,\,\,\,\\\\\\\begin{array}{*{20}{c}}{}\\{143}\\\begin{array}{l}\underline {\,\,\,\,140\,\,\,\,\,} \\\,\,\,\,3\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,5\,\,\,} }\\{28}\end{array}} \right.}\\{}\end{array}\,\,\,\,\,\,\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{}\\{143}\\\begin{array}{l}\underline {\,\,\,140\,\,\,\,} \\\,\,\,\,3\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,7\,\,\,} }\\{20}\end{array}} \right.}\\{}\end{array}\\\\\begin{array}{*{20}{c}}{}\\{143}\\\begin{array}{l}\underline {\,\,\,\,140\,\,\,\,\,} \\\,\,\,\,0\end{array}\end{array}\begin{array}{*{20}{c}}{}\\{\left| {\begin{array}{*{20}{c}}{\underline {\,\,\,11\,\,\,} }\\{13}\end{array}} \right.}\\{}\end{array}\end{array}\)

چون بر عدد 11 تقسیم پذیر می باشد، پس عدد مرکّب است.