Решебник по алгебре 8 класс Мерзляк Задание 605

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\[1)\ \sqrt{8 - 2\sqrt{7}} = \sqrt{1 - 2\sqrt{7} + 7} =\]

\[= \sqrt{\left( 1 - \sqrt{7} \right)^{2}} = \left| 1 - \sqrt{7} \right| =\]

\[= \sqrt{7} - 1\ \]

\[2)\ \sqrt{5 - 2\sqrt{6}} = \sqrt{3 - 2\sqrt{6} + 2} =\]

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

\[= \sqrt{3} - \sqrt{2}\]

\[3)\ \sqrt{12 - 6\sqrt{3}} = \sqrt{9 - 6\sqrt{3} + 3} =\]

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

\[= 3 - \sqrt{3}\]

\[4)\ \sqrt{38 - 12\sqrt{2}} =\]

\[= \sqrt{36 - 12\sqrt{2} + 2} =\]

\[= \sqrt{\left( 6 - \sqrt{2} \right)^{2}} = \left| 6 - \sqrt{2} \right| =\]

\[= 6 - \sqrt{2}\]