Question

efectuati calculele

va rog mult,dau coroana

Answer 1

 

$\displaystyle\bf\\ \sqrt{\frac{128}{49}}+\sqrt{\frac{288}{196}}-\sqrt{\frac{162}{441}}+\sqrt{\frac{242}{784}}=\\\\\\=\sqrt{\frac{64\times2}{49}}+\sqrt{\frac{144\times2}{196}}-\sqrt{\frac{81\times2}{441}}+\sqrt{\frac{121\times2}{784}}=\\\\\\=\sqrt{\frac{8^2\times2}{7^2}}+\sqrt{\frac{12^2\times2}{14^2}}-\sqrt{\frac{9^2\times2}{21^2}}+\sqrt{\frac{11^2\times2}{28^2}}=$

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$\displaystyle\bf\\=\frac{8\sqrt{2}}{7}+\frac{12\sqrt{2}}{14}-\frac{9\sqrt{2}}{21}+\frac{11\sqrt{2}}{28}=\\\\\\=\frac{^{4)}8\sqrt{2}}{7}+\frac{^{4)}6\sqrt{2}}{7}-\frac{^{4)}3\sqrt{2}}{7}+\frac{11\sqrt{2}}{28}=\\\\\\=\frac{32\sqrt{2}}{28}+\frac{24\sqrt{2}}{28}-\frac{12\sqrt{2}}{28}+\frac{11\sqrt{2}}{28}=\\\\\\=\frac{32\sqrt{2}+24\sqrt{2}-12\sqrt{2}+11\sqrt{2}}{28}=\\\\\\=\boxed{\bf\frac{55\sqrt{2}}{28}}$

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$\displaystyle\bf\\d)\\\\\sqrt{\frac{96}{196}}-\sqrt{\frac{150}{49}}+\sqrt{\frac{864}{441}}-\sqrt{\frac{1176}{1225}}=\\\\\\=\sqrt{\frac{16\times6}{196}}-\sqrt{\frac{25\times6}{49}}+\sqrt{\frac{144\times6}{441}}-\sqrt{\frac{196\times6}{1225}}=\\\\\\=\sqrt{\frac{4^2\times6}{14^2}}-\sqrt{\frac{5^2\times6}{7^2}}+\sqrt{\frac{12^2\times6}{21^2}}-\sqrt{\frac{14^2\times6}{35^2}}=$

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$\displaystyle\bf\\=\frac{4\sqrt{6}}{14}-\frac{5\sqrt{6}}{7}+\frac{12\sqrt{6}}{21}-\frac{14\sqrt{6}}{35}=\\\\\\=\frac{^{5)}2\sqrt{6}}{7}-\frac{^{5)}5\sqrt{6}}{7}+\frac{^{5)}4\sqrt{6}}{7}-\frac{14\sqrt{6}}{35}=\\\\\\=\frac{10\sqrt{6}}{35}-\frac{25\sqrt{6}}{35}+\frac{20\sqrt{6}}{35}-\frac{14\sqrt{6}}{35}=\\\\\\=\frac{10\sqrt{6}-25\sqrt{6}+20\sqrt{6}-14\sqrt{6}}{35}=\\\\\\=\boxed{\bf\frac{-9\sqrt{6}}{35}}$