Задание 5. Найдите значение выражения: 1 (√20-√5)√5; 2 (√18-√2)√2 3 (√48-√3) √3; 4 (√50+√2)-√2; 5 (√45+√5)√5; 6 (√27+√3)√3; 7 √5-18-√10; 8 √7-12-√21; 9 √2-45-√10; 10 √7-45-√35; 11 √11-32-√22; 12 √13-18-√26.

Решение:

1. \( (\sqrt{20} - \sqrt{5})\sqrt{5} = \sqrt{20}\sqrt{5} - \sqrt{5}\sqrt{5} = \sqrt{100} - 5 = 10 - 5 = 5 \)
2. \( (\sqrt{18} - \sqrt{2})\sqrt{2} = \sqrt{18}\sqrt{2} - \sqrt{2}\sqrt{2} = \sqrt{36} - 2 = 6 - 2 = 4 \)
3. \( (\sqrt{48} - \sqrt{3})\sqrt{3} = \sqrt{48}\sqrt{3} - \sqrt{3}\sqrt{3} = \sqrt{144} - 3 = 12 - 3 = 9 \)
4. \( (\sqrt{50} + \sqrt{2})\sqrt{2} = \sqrt{50}\sqrt{2} + \sqrt{2}\sqrt{2} = \sqrt{100} + 2 = 10 + 2 = 12 \)
5. \( (\sqrt{45} + \sqrt{5})\sqrt{5} = \sqrt{45}\sqrt{5} + \sqrt{5}\sqrt{5} = \sqrt{225} + 5 = 15 + 5 = 20 \)
6. \( (\sqrt{27} + \sqrt{3})\sqrt{3} = \sqrt{27}\sqrt{3} + \sqrt{3}\sqrt{3} = \sqrt{81} + 3 = 9 + 3 = 12 \)
7. \( \sqrt{5} \cdot \sqrt{18} - \sqrt{10} = \sqrt{5 \cdot 18} - \sqrt{10} = \sqrt{90} - \sqrt{10} = \sqrt{9 \cdot 10} - \sqrt{10} = 3\sqrt{10} - \sqrt{10} = 2\sqrt{10} \)
8. \( \sqrt{7} \cdot \sqrt{12} - \sqrt{21} = \sqrt{7 \cdot 12} - \sqrt{21} = \sqrt{84} - \sqrt{21} = \sqrt{4 \cdot 21} - \sqrt{21} = 2\sqrt{21} - \sqrt{21} = \sqrt{21} \)
9. \( \sqrt{2} \cdot \sqrt{45} - \sqrt{10} = \sqrt{2 \cdot 45} - \sqrt{10} = \sqrt{90} - \sqrt{10} = \sqrt{9 \cdot 10} - \sqrt{10} = 3\sqrt{10} - \sqrt{10} = 2\sqrt{10} \)
10. \( \sqrt{7} \cdot \sqrt{45} - \sqrt{35} = \sqrt{7 \cdot 45} - \sqrt{35} = \sqrt{315} - \sqrt{35} = \sqrt{9 \cdot 35} - \sqrt{35} = 3\sqrt{35} - \sqrt{35} = 2\sqrt{35} \)
11. \( \sqrt{11} \cdot \sqrt{32} - \sqrt{22} = \sqrt{11 \cdot 32} - \sqrt{22} = \sqrt{352} - \sqrt{22} = \sqrt{16 \cdot 22} - \sqrt{22} = 4\sqrt{22} - \sqrt{22} = 3\sqrt{22} \)
12. \( \sqrt{13} \cdot \sqrt{18} - \sqrt{26} = \sqrt{13 \cdot 18} - \sqrt{26} = \sqrt{234} - \sqrt{26} = \sqrt{9 \cdot 26} - \sqrt{26} = 3\sqrt{26} - \sqrt{26} = 2\sqrt{26} \)

Ответ: 1. 5; 2. 4; 3. 9; 4. 12; 5. 20; 6. 12; 7. 2√10; 8. √21; 9. 2√10; 10. 2√35; 11. 3√22; 12. 2√26.