1.
[tex]\it 0,09=\dfrac{9}{100}\in\mathbb{Q}\\ \\ \\ 3+\sqrt9=3+3=6=\dfrac{6}{1}\in\mathbb{Q}\\ \\ \\ 2^{3^2}=2^9=512=\dfrac{512}{1}\in\mathbb{Q}\\ \\ \\ \sqrt{12}-2\sqrt3=\sqrt{4\cdot3}-2\sqrt3=2\sqrt3-2\sqrt3=0=\dfrac{0}{1}\in\mathbb{Q}\\ \\ \\ \\ \dfrac{-1}{\sqrt{16}}=-\dfrac{1}{4}\in\mathbb{Q}\\ \\ \\ 23=\dfrac{23}{1}\in\mathbb{Q}[/tex]
2.
a)
[tex]\it x\in(1,\ \ \infty)|_{\cdot5} \Rightarrow 5x\in(5,\ \ \infty)\\ \\ y\in(2,\ \ \infty)|_{\cdot3} \Rightarrow 3y\in(6,\ \ \infty)\\\rule{140}{0.6}\\\rule{0.3}{0.3}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5x+6y\in(11,\ \ \infty)[/tex]
b)
[tex]\it y\in(2,\ \ \infty) \Rightarrow y^2\in(4,\ \ \infty)|_{\cdot3} \Rightarrow 3y^2\in(12,\ \ \infty)[/tex]
