The product of any two irrational numbers is

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.
$\frac{6}{\sqrt{6}}$

Express $0.7\overline{39}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Insert a rational number and an irrational number between the following:
$6.375289$ and $6.375738$

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

Are there two irrational numbers whose sum and product both are rational? Justify.