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 $\boxed{11\ \textless \ \sqrt{130}\ \textless \ 12}$

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.