Question

Is the square root of 130 rational or irrational? and where would it be located on a number line?

Answer 1

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 \ √(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.