Let's start by the easiest question, the second.
We knoa that \(11^2=121\ \textless \ 130\ \textless \ 12^2=144\) hence \(\boxed{11\ \textless \ \sqrt{130}\ \textless \ 12}\)
Now let's try simplifying the square root of \(130\) : \(130=2\cdot5\cdot13\), which are all prime numbers that appear only once : the square root of 130 is irrational.
