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1 عبارت های زیر را با هم مقایسه کنید:
\(\left| {{{\left( { - 7} \right)}^2}} \right|\;\bigcirc \;{\left| { - 7} \right|^2}\) الف
\(\left| { - 8 + 5} \right|\;\bigcirc \;\left| { - 8} \right| + \left| 5 \right|\) ب
\(\left| {3 - 9} \right|\;\bigcirc \;\left| 3 \right| - \left| 9 \right|\) ج
الف
\(\begin{array}{l}\left| {{{\left( { - 7} \right)}^2}} \right|\; = \left| {49} \right|\; = 49\\\\{\left| { - 7} \right|^2} = {(7)^2}\; = 49\\\\ \Rightarrow \left| {{{\left( { - 7} \right)}^2}} \right|\; = \;{\left| { - 7} \right|^2}\end{array}\)
ب
\(\begin{array}{l}\left| { - 8 + 5} \right| = \left| { - 3} \right| = 3\\\\\left| { - 8} \right| + \left| 5 \right| = 8 + 5 = 13\\\\ \Rightarrow \left| { - 8 + 5} \right|\; < \;\left| { - 8} \right| + \left| 5 \right|\end{array}\)
ج
\(\begin{array}{l}\left| {3 - 9} \right| = \left| { - 6} \right| = 6\\\\\left| 3 \right| - \left| 9 \right| = 3 - 9 = - 6\\\\ \Rightarrow \left| {3 - 9} \right|\; > \;\left| 3 \right| - \left| 9 \right|\end{array}\)
2 عبارات زیر را بدون استفاده از قدرمطلق بنویسید:
\(\begin{array}{l}\left| {\;0\;} \right| = \;\\\\\left| { - \frac{4}{3}} \right| = \\\\\left| {{7^3} - {7^4}} \right| = \\\\\left| {0/{2^5} - 0/{2^6}} \right| = \end{array}\)
\(\begin{array}{l}\left| {\;0\;} \right| = \;0\\\\\left| { - \frac{4}{3}} \right| = \frac{4}{3}\\\\\left| {{7^3} - {7^4}} \right| = - ({7^3} - {7^4}) = {7^4} - {7^3}\\\\\left| {0/{2^5} - 0/{2^6}} \right| = 0/{2^5} - 0/{2^6}\end{array}\)
3 حاصل عبارات زیر رابه دست آورید:
\(\sqrt {{{\left( { - 2595} \right)}^2}} = \) الف
ب \(\sqrt {{{\left( {1394} \right)}^2}} = \)
ج \(\sqrt {{{\left( { - 3 + \sqrt {10} } \right)}^2}} = \)
د \(\sqrt {{{\left( {2 - \sqrt 5 } \right)}^2}} = \)
الف
\(\sqrt {{{\left( { - 2595} \right)}^2}} = \left| { - 2595} \right| = 2595\)
ب
\(\sqrt {{{\left( {1394} \right)}^2}} = \left| {1394} \right| = 1394\)
ج
\(\sqrt {{{\left( { - 3 + \sqrt {10} } \right)}^2}} = \left| { - 3 + \sqrt {10} } \right| = \sqrt {10} - 3\)
د
\(\sqrt {{{\left( {2 - \sqrt 5 } \right)}^2}} = \left| {2 - \sqrt 5 } \right| = \sqrt 5 - 2\)
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