ГДЗ по алгебре 8 класс Макарычев Задание 445

\[\boxed{\text{445\ (445).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \sqrt{11 + 6\sqrt{2}} - \sqrt{2} =\]

\[= \sqrt{9 + 2 + 6\sqrt{2}} - \sqrt{2} =\]

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

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

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

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

\[= 3\ \left( так\ как\ 3 + \sqrt{2} > 0 \right).\]

\[\textbf{б)}\ \sqrt{27 - 5\sqrt{8}} + \sqrt{2} =\]

\[= \sqrt{27 - 5 \cdot 2\sqrt{2}} + \sqrt{2} =\]

\[= \sqrt{27 - 10\sqrt{2}} + \sqrt{2} =\]

\[= \sqrt{25 + 2 - 10\sqrt{2}} + \sqrt{2} =\]

\[= \sqrt{5^{2} - 2 \cdot 5\sqrt{2} + \left( \sqrt{2} \right)^{2}} =\]

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

\[= \left| 5 - \sqrt{2} \right| + \sqrt{2} =\]

\[= 5 - \sqrt{2} + \sqrt{2} =\]

\[= 5\ \left( так\ как\ 5 = \sqrt{25} > \sqrt{2} \right).\]