Which of the following is true about set $A$?

$A=\{m+n \cdot 2^{1/2} : m, n \text{ are integers}\}$

- $A$ is dense in $\mathbb R$.
- $A$ has only countable number of limit point in $\mathbb R$.
- $A$ has no limit point in $\mathbb R$.
- Only irrational number is limit point of $A$.

please explain.