1. დავიწყოთ პირველი შეკითხვით: გამარტივება \(\sqrt{\frac{0.64 \times 81}{49}}\).\n 2. გამოვიყენოთ წესი: \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\) და \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\).\n 3. გამოთვალოთ ცალკე: \(\sqrt{0.64} = 0.8\), \(\sqrt{81} = 9\), \(\sqrt{49} = 7\).\n 4. ამიტომ \(\sqrt{\frac{0.64 \times 81}{49}} = \frac{0.8 \times 9}{7} = \frac{7.2}{7} = 1.028571...\) მაგრამ უკეთესი ფორმით: \(\frac{0.8 \times 9}{7} = \frac{7.2}{7}\).\n 5. მეორე გამოთვლა: \(\sqrt{\frac{169 \times 81}{400}} = \frac{\sqrt{169} \times \sqrt{81}}{\sqrt{400}} = \frac{13 \times 9}{20} = \frac{117}{20} = 5.85\).\n 6. მესამე: \(\sqrt{\frac{9}{16} \times \frac{1}{25}} = \sqrt{\frac{9 \times 1}{16 \times 25}} = \sqrt{\frac{9}{400}} = \frac{3}{20} = 0.15\).\n 7. მეოთხე: \(\sqrt{\frac{64}{49} \times \frac{4}{9}} = \sqrt{\frac{64 \times 4}{49 \times 9}} = \sqrt{\frac{256}{441}} = \frac{16}{21} \approx 0.7619\).\n 8. მეორე ნაწილი: \(\sqrt{3^{12}} = 3^{6}\) რადგან \(\sqrt{a^b} = a^{b/2}\).\n 9. \(\sqrt{5^{24}} = 5^{12}\).\n 10. \(\sqrt{3^{100} \times 2^{40}} = \sqrt{3^{100}} \times \sqrt{2^{40}} = 3^{50} \times 2^{20}\).\n 11. \(\sqrt{24^{2} \times 3^{2}} = \sqrt{(24 \times 3)^2} = 24 \times 3 = 72\).\n 12. მესამე ნაწილი: \(\sqrt{15^{2} \times 15^{6}} = \sqrt{15^{8}} = 15^{4}\).\n 13. \(\sqrt{2^{4} \times 7^{4} \times 5^{4}} = \sqrt{(2 \times 7 \times 5)^{4}} = (2 \times 7 \times 5)^{2} = 70^{2} = 4900\).\n 14. \(\sqrt{\frac{7^{4}}{2^{6} \times 5^{6}}} = \frac{7^{2}}{2^{3} \times 5^{3}} = \frac{49}{8 \times 125} = \frac{49}{1000} = 0.049\).\n 15. \(\sqrt{\frac{3^{2} \times 2^{8}}{5^{4}}} = \frac{3^{1} \times 2^{4}}{5^{2}} = \frac{3 \times 16}{25} = \frac{48}{25} = 1.92\).\n 16. მეოთხე შეკითხვა: \(\sqrt{8 \times 98} = \sqrt{784} = 28\).\n 17. \(\sqrt{48 \times 27} = \sqrt{1296} = 36\).\n 18. \(\sqrt{810 \times 10} = \sqrt{8100} = 90\).\n 19. \(\sqrt{50} \times \sqrt{800} = \sqrt{50 \times 800} = \sqrt{40000} = 200\).\n 20. \(\sqrt{50} \times 72 = 72 \times \sqrt{50} = 72 \times 5 \sqrt{2} = 360 \sqrt{2}\).\n 21. \(\sqrt{32} \times 162 = 162 \times \sqrt{32} = 162 \times 4 \sqrt{2} = 648 \sqrt{2}\).\n 22. \(\sqrt{2} \times \sqrt{98} = \sqrt{2 \times 98} = \sqrt{196} = 14\).\n 23. \(\sqrt{5} \times \sqrt{45} = \sqrt{225} = 15\).\n 24. \(\sqrt{242} \times \sqrt{8} = \sqrt{242 \times 8} = \sqrt{1936} = 44\).\n საბოლოო პასუხები:\n ა) \(\frac{7.2}{7}, 5.85, 0.15, \frac{16}{21}\)\n ბ) \(3^{6}, 5^{12}, 3^{50} \times 2^{20}, 72\)\n გ) \(15^{4}, 4900, \frac{49}{1000}, \frac{48}{25}\)\n 41.\n ა) 28, 36, 90\n ბ) 200, 360 \sqrt{2}, 648 \sqrt{2}\n გ) 14, 15, 44