دانلود اپلیکیشن
حاصل عبارت های زیر را ساده کنید.
راه حل ها را توضیح دهید و آنها را کامل کنید.
\(\sqrt {72} - \sqrt {32} + \sqrt {18} \) الف
ابتدا حاصل هریک از رادیکال ها را به دست می آوریم :
(جاهای خالی را کامل کنید)
\(\begin{array}{l}\sqrt {72} = \sqrt {{6^2} \times 2} = 6\sqrt {\,\,\,\,\,\,} \\\\\sqrt {32} = \sqrt {{4^2} \times \,\,\,} = 4\sqrt {\,\,\,\,\,\,} \\\\\sqrt {18} = \sqrt {\,\,\,\,\,\,\,\,} = 3\sqrt 2 \\\\ \Rightarrow \sqrt {72} - \sqrt {32} + \sqrt {18} = 6\sqrt {\,\,\,\,\,\,} - \,\,\,\,\,\,\,\,\,\,\,\, + \,\,\,\,\,\,\,\,\,\,\,\,\,5\sqrt 2 \end{array}\)
ب
\(\begin{array}{l}\sqrt {50} + \sqrt[3]{{24}} + \sqrt[3]{{81}} = \sqrt {{5^2} \times 2} + \sqrt[3]{{{2^3} \times 3}} + \sqrt[3]{{{3^3} \times 3}}\\\\\\ = 5\sqrt {\,\,\,\,\,\,} + 2\sqrt[3]{{\,\,\,\,\,\,}} + 3\sqrt[3]{{\,\,\,\,\,\,\,\,}} = 5\sqrt {\,\,\,\,\,\,} + 5\sqrt[3]{{\,\,\,\,\,\,\,\,}}\end{array}\)
الف
\(\begin{array}{l}\sqrt {72} = \sqrt {{6^2} \times 2} = 6\sqrt 2 \\\\\sqrt {32} = \sqrt {{4^2} \times \,2} = 4\sqrt 2 \\\\\sqrt {18} = \sqrt {{3^2} \times 2} = 3\sqrt 2 \\\\ \Rightarrow \sqrt {72} - \sqrt {32} + \sqrt {18} = 6\sqrt 2 - 4\sqrt 2 + \,3\sqrt 2 = 5\sqrt 2 \end{array}\)
ب
\(\begin{array}{l}\sqrt {50} + \sqrt[3]{{24}} + \sqrt[3]{{81}} = \sqrt {{5^2} \times 2} + \sqrt[3]{{{2^3} \times 3}} + \sqrt[3]{{{3^3} \times 3}}\\\\ = 5\sqrt 2 + 2\sqrt[3]{3} + 3\sqrt[3]{3} = 5\sqrt 2 + 5\sqrt[3]{3}\end{array}\)
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