8. Найдите значение выражения 1 $$\frac{(7\sqrt{11})^2}{110}$$; 2 $$\frac{48}{(2\sqrt{6})^2}$$; 3 $$\left(\sqrt{23}-4\right)\left(\sqrt{23}+4\right)$$; 4 $$\left(\sqrt{15}-\sqrt{7}\right)\left(\sqrt{15}+ \sqrt{7}\right)$$; 5 $$\left(\sqrt{14}-3\right)^2+6\sqrt{14}$$; 6 $$\frac{1}{4+\sqrt{14}}+\frac{1}{4-\sqrt{14}}$$; 7 $$\frac{1}{\sqrt{37}-6} - \frac{1}{\sqrt{37}+6}$$

8. Найдите значение выражения

1. $$\frac{(7\sqrt{11})^2}{110}$$;
$$\frac{(7\sqrt{11})^2}{110} = \frac{49 \cdot 11}{110} = \frac{49 \cdot 1}{10} = 4.9$$
2. $$\frac{48}{(2\sqrt{6})^2}$$;
$$\frac{48}{(2\sqrt{6})^2} = \frac{48}{4 \cdot 6} = \frac{48}{24} = 2$$
3. $$\left(\sqrt{23}-4\right)\left(\sqrt{23}+4\right)$$;
$$\left(\sqrt{23}-4\right)\left(\sqrt{23}+4\right) = (\sqrt{23})^2 - 4^2 = 23 - 16 = 7$$
4. $$\left(\sqrt{15}-\sqrt{7}\right)\left(\sqrt{15}+ \sqrt{7}\right)$$;
$$\left(\sqrt{15}-\sqrt{7}\right)\left(\sqrt{15}+ \sqrt{7}\right) = (\sqrt{15})^2 - (\sqrt{7})^2 = 15 - 7 = 8$$
5. $$\left(\sqrt{14}-3\right)^2+6\sqrt{14}$$;
$$\left(\sqrt{14}-3\right)^2+6\sqrt{14} = (\sqrt{14})^2 - 2\cdot3\sqrt{14} + 3^2 + 6\sqrt{14} = 14 - 6\sqrt{14} + 9 + 6\sqrt{14} = 23$$
6. $$\frac{1}{4+\sqrt{14}}+\frac{1}{4-\sqrt{14}}$$;
$$\frac{1}{4+\sqrt{14}}+\frac{1}{4-\sqrt{14}} = \frac{4-\sqrt{14} + 4 + \sqrt{14}}{(4+\sqrt{14})(4-\sqrt{14})} = \frac{8}{16 - 14} = \frac{8}{2} = 4$$
7. $$\frac{1}{\sqrt{37}-6} - \frac{1}{\sqrt{37}+6}$$
$$\frac{1}{\sqrt{37}-6} - \frac{1}{\sqrt{37}+6} = \frac{\sqrt{37}+6 - (\sqrt{37}-6)}{(\sqrt{37}-6)(\sqrt{37}+6)} = \frac{\sqrt{37}+6 - \sqrt{37}+6}{37 - 36} = \frac{12}{1} = 12$$

Ответ:

1. 4.9
2. 2
3. 7
4. 8
5. 23
6. 4
7. 12