The conjugate surd of $3+\sqrt{2}$ is $\ldots \ldots \ldots \ldots .$

Prove that $3+2 \sqrt{5}$ is an irrational number.

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

Show that the square of an odd positive integer can be of the form $6q + 1$ or $6q + 3$ for some integer $q$.

Four bells toll at intervals of $8$,$12$,$15$,and $18$ seconds respectively. All four begin to toll together. How many times will they toll together in one hour,excluding the one at the start?

Prove that $n^{2}-n$ is divisible by $2$ for every positive integer $n$.