Задание 5. Найдите значение

Решение:

1. \( (\sqrt{20} - \sqrt{5}) \cdot \sqrt{5} = (\sqrt{4 \cdot 5} - \sqrt{5}) \cdot \sqrt{5} = (2\sqrt{5} - \sqrt{5}) \cdot \sqrt{5} = \sqrt{5} \cdot \sqrt{5} = 5 \)


2. \( (\sqrt{18} - \sqrt{2}) \cdot \sqrt{2} = (\sqrt{9 \cdot 2} - \sqrt{2}) \cdot \sqrt{2} = (3\sqrt{2} - \sqrt{2}) \cdot \sqrt{2} = 2\sqrt{2} \cdot \sqrt{2} = 2 \cdot 2 = 4 \)


3. \( (\sqrt{48} - \sqrt{3}) \cdot \sqrt{3} = (\sqrt{16 \cdot 3} - \sqrt{3}) \cdot \sqrt{3} = (4\sqrt{3} - \sqrt{3}) \cdot \sqrt{3} = 3\sqrt{3} \cdot \sqrt{3} = 3 \cdot 3 = 9 \)


4. \( (\sqrt{50} + \sqrt{2}) \cdot \sqrt{2} = (\sqrt{25 \cdot 2} + \sqrt{2}) \cdot \sqrt{2} = (5\sqrt{2} + \sqrt{2}) \cdot \sqrt{2} = 6\sqrt{2} \cdot \sqrt{2} = 6 \cdot 2 = 12 \)


5. \( (\sqrt{45} + \sqrt{5}) \cdot \sqrt{5} = (\sqrt{9 \cdot 5} + \sqrt{5}) \cdot \sqrt{5} = (3\sqrt{5} + \sqrt{5}) \cdot \sqrt{5} = 4\sqrt{5} \cdot \sqrt{5} = 4 \cdot 5 = 20 \)


6. \( (\sqrt{27} + \sqrt{3}) \cdot \sqrt{3} = (\sqrt{9 \cdot 3} + \sqrt{3}) \cdot \sqrt{3} = (3\sqrt{3} + \sqrt{3}) \cdot \sqrt{3} = 4\sqrt{3} \cdot \sqrt{3} = 4 \cdot 3 = 12 \)

Ответ: 1. 5; 2. 4; 3. 9; 4. 12; 5. 20; 6. 12.