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Ответ:
Решение:
- а) \(\frac{\sqrt{363}}{\sqrt{3}} = \sqrt{\frac{363}{3}} = \sqrt{121} = 11\)
- б) \(\frac{\sqrt{512}}{\sqrt{32}} = \sqrt{\frac{512}{32}} = \sqrt{16} = 4\)
- в) \(\frac{\sqrt{252}}{\sqrt{700}} = \sqrt{\frac{252}{700}} = \sqrt{\frac{126}{350}} = \sqrt{\frac{63}{175}} = \sqrt{\frac{9}{25}} = \frac{3}{5} = 0.6\)
- г) \(\frac{\sqrt{405}}{\sqrt{500}} = \sqrt{\frac{405}{500}} = \sqrt{\frac{81}{100}} = \frac{9}{10} = 0.9\)
- а) \(\frac{\sqrt{75} \cdot \sqrt{32}}{\sqrt{24}} = \frac{\sqrt{75 \cdot 32}}{\sqrt{24}} = \sqrt{\frac{75 \cdot 32}{24}} = \sqrt{\frac{3 \cdot 25 \cdot 4 \cdot 8}{3 \cdot 8}} = \sqrt{25 \cdot 4} = \sqrt{100} = 10\)
- е) \(\frac{\sqrt{98} \cdot \sqrt{125}}{\sqrt{40}} = \frac{\sqrt{98 \cdot 125}}{\sqrt{40}} = \sqrt{\frac{98 \cdot 125}{40}} = \sqrt{\frac{(2 \cdot 49) \cdot 125}{5 \cdot 8}} = \sqrt{\frac{2 \cdot 49 \cdot 5 \cdot 25}{5 \cdot 8}} = \sqrt{\frac{49 \cdot 25 \cdot 2}{8}} = \sqrt{\frac{49 \cdot 25}{4}} = \frac{7 \cdot 5}{2} = \frac{35}{2} = 17.5\)
- ж) \(\frac{\sqrt{2100}}{\sqrt{48} \cdot \sqrt{28}} = \frac{\sqrt{2100}}{\sqrt{48 \cdot 28}} = \sqrt{\frac{2100}{48 \cdot 28}} = \sqrt{\frac{2100}{1344}} = \sqrt{\frac{1050}{672}} = \sqrt{\frac{525}{336}} = \sqrt{\frac{175}{112}} = \sqrt{\frac{25}{16}} = \frac{5}{4} = 1.25\)
- з) \(\frac{\sqrt{10800}}{\sqrt{15} \cdot \sqrt{80}} = \frac{\sqrt{10800}}{\sqrt{15 \cdot 80}} = \sqrt{\frac{10800}{1200}} = \sqrt{9} = 3\)
Ответ: а) 11; б) 4; в) 0.6; г) 0.9; а) 10; е) 17.5; ж) 1.25; з) 3.
