Express $0 . \overline{83}$ in the form $\frac{p}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$.
If $a=\frac{3+\sqrt{5}}{2},$ then find the value of $a^{2}+\frac{1}{a^{2}}$.
For each question, select the proper option from four options given, to make the statement true : (Final answer only)
$0.3 \overline{6}=$
The value of $1.999 ....$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0,$ is
Construct the square root spiral up to $\sqrt{6}$.