Is $\sqrt{8+15}$ a rational number or an irrational number?

Calculate the sum: $0.\overline{35} + 0.\overline{28}$.

Let $x$ and $y$ be rational and irrational numbers,respectively. Is $x+y$ necessarily an irrational number? Give an example in support of your answer.

Convert the following rational number into decimal form and state the kind of its decimal expansion:
$\frac{29}{12}$

Insert a rational number and an irrational number between the following: $\frac{1}{3}$ and $\frac{1}{2}$

Show that $0.1\overline{6} = \frac{1}{6}$.