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