If we can write this expression as a fraction, then this will be rational. Otherwise, irrational.
First, let's write the repeating decimal as fraction. Excluding the 1 point to the left of the decimal.
We have:
0.234523452345...
We can write it as:
[tex]\frac{2345}{9999}[/tex]Tagging along the "1", we have:
[tex]1\frac{2345}{9999}[/tex]Then, we have square root of 4, which is "2".
If we multiply the fraction shown above by 2, we will definitely have a fraction.
That will be a rational number.
