The decimal expansion of the rational number $\frac{33}{2^{2} \cdot 5}$ will terminate after

Prove that $\sqrt{p}+\sqrt{q}$ is irrational,where $p$ and $q$ are distinct prime numbers.

Three sets of English,Hindi,and Mathematics books have to be stacked in such a way that all the books are stored topic-wise and the height of each stack is the same. The number of English books is $96$,the number of Hindi books is $240$,and the number of Mathematics books is $336$. Assuming that the books are of the same thickness,determine the number of stacks of English,Hindi,and Mathematics books.

The following real number is expressed in decimal form. Determine whether it is rational or not. If it is rational,express it in the form of $\frac{p}{q}$. $18.484848 \ldots$

Find the square root of $12-\sqrt{140}$.

Write the denominator of the rational number $\frac{257}{5000}$ in the form $2^{m} \times 5^{n},$ where $m, n$ are non-negative integers. Hence,write its decimal expansion,without actual division.