Find the $\text{g.c.d.}$ (Greatest Common Divisor) of $196$ and $38220$ using Euclid's division algorithm.

Find the $G$.$C$.$D$. of $(28, 35, 91)$.

$A$ positive integer is of the form $3q + 1$,where $q$ is a natural number. Can you write its square in any form other than $3m + 1$,i.e.,$3m$ or $3m + 2$ for some integer $m$? Justify your answer.

Find the square root of $3-\sqrt{5}$.

Prove that $\sqrt{2}+\sqrt{3}$ is irrational.

Find the $\text{g.c.d.}$ and $\text{l.c.m.}$ of $510$ and $92$ using the fundamental theorem of arithmetic.