Question

Can anyone help me out with this?

Answer 1

$\sqrt{2} + \frac{3}{ \sqrt{2} }$
$= \frac{2 + 3}{ \sqrt{2} }$
$= \frac{5}{ \sqrt{2} }$
now multiplying both the numerator and denominator by root over 2
$= \frac{5 \sqrt{2} }{2}$
$= 2.5 \times 1.41421...$
= 3.53553...
which is not exact number.
hence it is Irrational number.