Решебник по алгебре 8 класс Мерзляк ФГОС Задание 524

 

\[\boxed{\mathbf{524\ (524).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2};\]

\[2)\ \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3};\]

\[3)\ \sqrt{32} = \sqrt{4 \cdot 8} = \sqrt{16 \cdot 2} = 4\sqrt{2};\]

\[4)\ \sqrt{54} = \sqrt{9 \cdot 6} = 3\sqrt{6};\]

\[5)\ \sqrt{490} = \sqrt{49 \cdot 10} = 7\sqrt{10};\]

\[6)\ \sqrt{500} = \sqrt{100 \cdot 5} = 10\sqrt{5};\]

\[7)\ \sqrt{275} = \sqrt{25 \cdot 11} = 5\sqrt{11};\]

\[8)\ \sqrt{108} = \sqrt{36 \cdot 3} = 6\sqrt{3};\]

\[9)\ \sqrt{0,72} = \sqrt{9 \cdot 0,08} =\]

\[= \sqrt{9 \cdot 4 \cdot 0,02} = 6\sqrt{0,02} =\]

\[= 6\sqrt{\frac{2}{100}} = 0,6\sqrt{2};\]

\[10)\ \sqrt{0,48} = \sqrt{16 \cdot 0,03} =\]

\[= 4\sqrt{0,03} = 0,4\sqrt{3};\]

\[11)\ \sqrt{450} = \sqrt{225 \cdot 2} = 15\sqrt{2};\]

\[12)\ \sqrt{36300} = \sqrt{100 \cdot 121 \cdot 3} =\]

\[= 110\sqrt{3}\text{.\ }\]

\[\boxed{\mathbf{52}\mathbf{4}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ \sqrt{9 \cdot 25} = \sqrt{9} \cdot \sqrt{25} =\]

\[= 3 \cdot 5 = 15.\]

\[2)\ \sqrt{16 \cdot 2500} = \sqrt{16} \cdot \sqrt{2500} =\]

\[= 4 \cdot 50 = 200.\]

\[3)\ \sqrt{0,64 \cdot 36} = \sqrt{0,64} \cdot \sqrt{36} =\]

\[= 0,8 \cdot 6 = 4,8.\]

\[4)\ \sqrt{400 \cdot 1,44} =\]

\[= \sqrt{400} \cdot \sqrt{1,44} = 20 \cdot 1,2 = 24.\]

\[5)\ \sqrt{0,09 \cdot 0,04} =\]

\[= \sqrt{0,09} \cdot \sqrt{0,04} =\]

\[= 0,3 \cdot 0,2 = 0,06.\]

\[6)\ \sqrt{6,25 \cdot 0,16} =\]

\[= \sqrt{6,25} \cdot \sqrt{0,16} = 2,5 \cdot 0,4 = 1.\]

\[7)\ \sqrt{6^{2} \cdot 3^{4}} = \sqrt{6^{2}} \cdot \sqrt{3^{4}} =\]

\[= 6 \cdot 3^{2} = 6 \cdot 9 = 54.\]

\[8)\ \sqrt{7^{2} \cdot 2^{8}} = \sqrt{7^{2}} \cdot \sqrt{2^{8}} =\]

\[= 7 \cdot 2^{4} = 7 \cdot 16 = 112.\]

\[9)\ \sqrt{25 \cdot 64 \cdot 0,36} =\]

\[= \sqrt{25} \cdot \sqrt{64} \cdot \sqrt{0,36} =\]

\[= 5 \cdot 8 \cdot 0,6 = 24.\]

\[10)\ \sqrt{0,01 \cdot 0,81 \cdot 2500} =\]

\[= \sqrt{0,01} \cdot \sqrt{0,81} \cdot \sqrt{2500} =\]

\[= 0,1 \cdot 0,9 \cdot 50 = 4,5.\]

\[11)\ \sqrt{\frac{81}{100}} = \frac{\sqrt{81}}{\sqrt{100}} = \frac{9}{10} = 0,9.\]

\[12)\ \sqrt{\frac{49}{256}} = \frac{\sqrt{49}}{\sqrt{256}} = \frac{7}{16}.\]

\[13)\ \sqrt{3\frac{13}{36}} = \sqrt{\frac{121}{36}} = \frac{\sqrt{121}}{\sqrt{36}} =\]

\[= \frac{11}{6} = 1\frac{5}{6}.\]

\[14)\ \sqrt{3\frac{1}{16} \cdot 2\frac{14}{25}} = \sqrt{\frac{49}{16} \cdot \frac{64}{25}} =\]

\[= \frac{\sqrt{49} \cdot \sqrt{64}}{\sqrt{16} \cdot \sqrt{25}} = \frac{7 \cdot 8}{4 \cdot 5} = \frac{7 \cdot 2}{1 \cdot 5} =\]

\[= \frac{14}{5} = 2\frac{4}{5}.\]

\[15)\ \sqrt{\frac{169}{36 \cdot 81}} = \frac{\sqrt{169}}{\sqrt{36} \cdot \sqrt{81}} =\]

\[= \frac{13}{6 \cdot 9} = \frac{13}{54}.\]