The rationalising factor of $5 \sqrt{2}$ is ..............

The following real number has a decimal expansion as given below. Decide whether it is rational or not. If it is rational,and of the form $\frac{p}{q}$,what can you say about the prime factors of $q$?
$43. \overline{123456789}$

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

Write down the decimal expansion of the rational number $\frac{129}{2^{2} 5^{7} 7^{5}}$.

What type of decimal expansion is $0.9999...$? (Terminating,Non-terminating repeating,Non-terminating non-repeating)

$\sqrt{12-\sqrt{140}} = \dots$