Answer
Yes
Work Step by Step
$\sqrt 2$ and $\frac{3}{2}$ are located in the interval 1 to 2
The constant $e$ and $\frac{7}{3}$ are located in the interval 2 to 3.
$\pi$ and $\frac{7}{2}$ are located in the interval 3 to 4
Any interval can contain both rational and irrational numbers because you can take any number and "shift" it over into the desired interval by some combination of multiplying, dividing, adding or subtracting.
