Решебник по алгебре 8 класс Мерзляк Задание 896

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\[1)\ \sqrt{\left( 10 - \sqrt{11} \right)^{2}} =\]

\[= \left| 10 - \sqrt{11} \right| = 10 - \sqrt{11}\]

\[2)\ \sqrt{\left( \sqrt{10} - 11 \right)^{2}} =\]

\[= \left| \sqrt{10} - 11 \right| = 11 - \sqrt{10}\]

\[3)\ \sqrt{\left( \sqrt{10} - \sqrt{11} \right)^{2}} =\]

\[= \left| \sqrt{10} - \sqrt{11} \right| = \sqrt{11} - \sqrt{10}\]

\[4)\ \sqrt{\left( 3 - \sqrt{6} \right)^{2}} + \sqrt{\left( 2 - \sqrt{6} \right)^{2}} =\]

\[= \left| 3 - \sqrt{6} \right| + \left| 2 - \sqrt{6} \right| =\]

\[= 3 - \sqrt{6} + \sqrt{6} - 2 = 1\]

\[5)\ \sqrt{\left( \sqrt{24} - 5 \right)^{2}} - \sqrt{\left( \sqrt{24} - 4 \right)^{2}} =\]

\[= \left| \sqrt{24} - 5 \right| - \left| \sqrt{24} - 4 \right| =\]

\[= 5 - \sqrt{24} - \sqrt{24} + 4 =\]

\[= 9 - 2\sqrt{24}\]