(√35-√5)(√5+√35) =

1) $(\sqrt{35}-\sqrt{5})(\sqrt{5}+\sqrt{35}) = (\sqrt{35}-\sqrt{5})(\sqrt{35}+\sqrt{5}) = (\sqrt{35})^2 - (\sqrt{5})^2 = 35 - 5 = 30$. 2) $(\sqrt{6}-5)^2 = (\sqrt{6})^2 - 2 \cdot 5 \cdot \sqrt{6} + 5^2 = 6 - 10\sqrt{6} + 25 = 31 - 10\sqrt{6}$. 3) $\frac{(3\sqrt{5})^2}{200} = \frac{9 \cdot 5}{200} = \frac{45}{200} = \frac{9}{40} = 0,225$. 4) $\frac{\sqrt{15} \cdot \sqrt{12}}{\sqrt{20}} = \sqrt{\frac{15 \cdot 12}{20}} = \sqrt{\frac{180}{20}} = \sqrt{9} = 3$. 5) $\frac{7 \cdot (3a^4)^2}{a^3 \cdot a^7} = \frac{7 \cdot 9 \cdot a^8}{a^{10}} = \frac{63}{a^2}$. При $a = \sqrt{42}$, $a^2 = 42$, тогда $\frac{63}{42} = \frac{3}{2} = 1,5$.