Fill in the blanks to make the following statement true: $\sqrt{49} = \ldots \ldots$

Let $x$ be a rational number and $y$ be an irrational number. Is $xy$ necessarily irrational? Justify your answer with an example.

State whether the following statements are true or false. Justify your answer.
$(i)$ $\frac{\sqrt{2}}{3}$ is a rational number.
$(ii)$ There are infinitely many integers between any two integers.

For each question,select the proper option from four options given,to make the statement true: If $(\sqrt{5}+3)^{2}=a+b \sqrt{5}$,then........

Insert a rational number and an irrational number between the following:
$0.0001$ and $0.001$

If $125^{x} = \frac{25}{5^{x}},$ then find the value of $x$.