7. Найдите значение выражения 1 $$\left(\sqrt{28}-\sqrt{7}\right)\cdot\sqrt{7}$$; 2 $$\sqrt{7}\cdot 12\cdot \sqrt{21}$$; 3 $$\frac{\sqrt{30}\cdot\sqrt{15}}{\sqrt{18}}$$; 4 $$4\sqrt{13}\cdot 2\sqrt{3}\cdot \sqrt{39}$$; 5 $$\sqrt{7^4}$$; 6 $$\sqrt{9^5}$$

7. Найдите значение выражения

1. $$\left(\sqrt{28}-\sqrt{7}\right)\cdot\sqrt{7}$$;
$$\left(\sqrt{28}-\sqrt{7}\right)\cdot\sqrt{7} = \left(\sqrt{4\cdot7}-\sqrt{7}\right)\cdot\sqrt{7} = \left(2\sqrt{7}-\sqrt{7}\right)\cdot\sqrt{7} = \sqrt{7}\cdot\sqrt{7} = 7$$
2. $$\sqrt{7}\cdot 12\cdot \sqrt{21}$$;
$$\sqrt{7}\cdot 12\cdot \sqrt{21} = 12\cdot\sqrt{7\cdot21} = 12\cdot\sqrt{7\cdot7\cdot3} = 12\cdot7\cdot\sqrt{3} = 84\sqrt{3}$$
3. $$\frac{\sqrt{30}\cdot\sqrt{15}}{\sqrt{18}}$$;
$$\frac{\sqrt{30}\cdot\sqrt{15}}{\sqrt{18}} = \frac{\sqrt{30\cdot15}}{\sqrt{18}} = \frac{\sqrt{2\cdot15\cdot15}}{\sqrt{2\cdot9}} = \frac{15\sqrt{2}}{3\sqrt{2}} = \frac{15}{3} = 5$$
4. $$4\sqrt{13}\cdot 2\sqrt{3}\cdot \sqrt{39}$$;
$$4\sqrt{13}\cdot 2\sqrt{3}\cdot \sqrt{39} = 8\sqrt{13\cdot3\cdot39} = 8\sqrt{13\cdot3\cdot3\cdot13} = 8\cdot13\cdot3 = 312$$
5. $$\sqrt{7^4}$$;
$$\sqrt{7^4} = 7^2 = 49$$
6. $$\sqrt{9^5}$$
$$\sqrt{9^5} = \sqrt{9^4\cdot9} = 9^2\sqrt{9} = 81\cdot3 = 243$$

Ответ:

1. 7
2. $$84\sqrt{3}$$
3. 5
4. 312
5. 49
6. 243