ГДЗ по алгебре 8 класс Макарычев Задание 491

\[\boxed{\text{491\ (491).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ 0,2\sqrt{200} < 10\sqrt{8}\]

\[0,2 \cdot 10\sqrt{2} < 10 \cdot 2\sqrt{2}\]

\[2\sqrt{2} < 20\sqrt{2}\]

\[\textbf{б)}\ 7\sqrt{\frac{32}{49}} = 0,8\sqrt{50}\]

\[7\sqrt{\frac{16 \cdot 2}{49}} = 0,8\sqrt{25 \cdot 2}\]

\[7 \cdot \frac{4}{7}\sqrt{2} = 0,8 \cdot 5\sqrt{2}\]

\[4\sqrt{2} = 4\sqrt{2}\]

\[\textbf{в)}\ 0,5\sqrt{108} < 9\sqrt{3}\]

\[0,5\sqrt{36 \cdot 3} < 9\sqrt{3}\]

\[0,5 \cdot 6\sqrt{3} < 9\sqrt{3}\]

\[3\sqrt{3} < 9\sqrt{3}\]

\[\textbf{г)}\frac{5}{2}\sqrt{63} < 4,5\sqrt{28}\]

\[\frac{5}{2}\sqrt{9 \cdot 7} < 4,5 \cdot \sqrt{4 \cdot 7}\]

\[\frac{15}{2}\sqrt{7} < 9\sqrt{7}\]

\[7,5\sqrt{7} < 9\sqrt{7}\]