Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 105

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

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

\[= \sqrt{2} - 1\ \]

\[2)\ \sqrt{4 + 2\sqrt{3}} = \sqrt{1 + 2\sqrt{3} + 3} =\]

\[= \sqrt{\left( 1 + \sqrt{3} \right)^{2}} = 1 + \sqrt{3}\]

\[3)\ \sqrt{7 + 2\sqrt{6}} = \sqrt{1 + 2\sqrt{6} + 6} =\]

\[= \sqrt{\left( 1 + \sqrt{6} \right)^{2}} = 1 + \sqrt{6}\]

\[4)\ \sqrt{11 - 2\sqrt{10}} =\]

\[= \sqrt{1 - 2\sqrt{10} + 10} =\]

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

\[= \left| 1 - \sqrt{10} \right| = \sqrt{10} - 1\]