Simplify: $\frac{3+\sqrt{6}}{17 \sqrt{3}-2 \sqrt{32}+3 \sqrt{18}-4 \sqrt{48}}$

State whether the following rational number has a terminating decimal expansion or not. If it has,then find it: $\frac{23}{200}$

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

$\frac{p}{q}$ is a rational number and for non-negative integers $m$ and $n$,$q = 2^{m} 5^{n}$ if and only if the decimal form of $\frac{p}{q}$ is $\ldots \ldots \ldots \ldots$

Prove that,if $a$ and $b$ are odd positive integers,then $a^{2} + b^{2}$ is even but not divisible by $4$.

Find the square root of $6+\sqrt{35}$ in the form of a binomial surd.