Задание 5. Найдите значение выражения: 1) \((\sqrt{20}-\sqrt{5})\cdot\sqrt{5}\); 2) \((\sqrt{18}-\sqrt{2})\cdot\sqrt{2}\); 3) \((\sqrt{48}-\sqrt{3})\cdot\sqrt{3}\); 4) \((\sqrt{50}+\sqrt{2})\cdot\sqrt{2}\); 5) \((\sqrt{45}+\sqrt{5})\cdot\sqrt{5}\); 6) \((\sqrt{27}+\sqrt{3})\cdot\sqrt{3}\); 7) \(\sqrt{5\cdot18}\cdot\sqrt{10}\); 8) \(\sqrt{7\cdot12}\cdot\sqrt{21}\); 9) \(\sqrt{2\cdot45}\cdot\sqrt{10}\); 10) \(\sqrt{7\cdot45}\cdot\sqrt{35}\); 11) \(\sqrt{11\cdot32}\cdot\sqrt{22}\); 12) \(\sqrt{13\cdot18}\cdot\sqrt{26}\).

Используем свойство: \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\).

1. \((\sqrt{20}-\sqrt{5})\cdot\sqrt{5}=\sqrt{100}-\sqrt{25}=10-5=5\).
2. \((\sqrt{18}-\sqrt{2})\cdot\sqrt{2}=\sqrt{36}-\sqrt{4}=6-2=4\).
3. \((\sqrt{48}-\sqrt{3})\cdot\sqrt{3}=\sqrt{144}-\sqrt{9}=12-3=9\).
4. \((\sqrt{50}+\sqrt{2})\cdot\sqrt{2}=\sqrt{100}+\sqrt{4}=10+2=12\).
5. \((\sqrt{45}+\sqrt{5})\cdot\sqrt{5}=\sqrt{225}+\sqrt{25}=15+5=20\).
6. \((\sqrt{27}+\sqrt{3})\cdot\sqrt{3}=\sqrt{81}+\sqrt{9}=9+3=12\).
7. \(\sqrt{5\cdot18}\cdot\sqrt{10}=\sqrt{900}=30\).
8. \(\sqrt{7\cdot12}\cdot\sqrt{21}=\sqrt{1764}=42\).
9. \(\sqrt{2\cdot45}\cdot\sqrt{10}=\sqrt{900}=30\).
10. \(\sqrt{7\cdot45}\cdot\sqrt{35}=\sqrt{11025}=105\).
11. \(\sqrt{11\cdot32}\cdot\sqrt{22}=\sqrt{7744}=88\).
12. \(\sqrt{13\cdot18}\cdot\sqrt{26}=\sqrt{6084}=78\).

Ответ: 1) 5; 2) 4; 3) 9; 4) 12; 5) 20; 6) 12; 7) 30; 8) 42; 9) 30; 10) 105; 11) 88; 12) 78.