Is $0.3\overline{7}$ a rational number or an irrational number?

Express $1.23\overline{4}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Fill in the blanks to make the following statement true:
$\sqrt{1 \frac{25}{144}} = \ldots$

Find three different irrational numbers between the rational numbers $\frac{3}{4}$ and $\frac{4}{5}$.

Find the value of the following expression correct to three decimal places,rationalizing the denominator if needed. Take $\sqrt{2} = 1.414$,$\sqrt{3} = 1.732$,and $\sqrt{5} = 2.236$.
$\frac{\sqrt{2}}{2+\sqrt{2}}$

For each question,select the proper option from the four options given to make the statement true: $0.\overline{3} = \dots$