Suppose $(\mathbb{R},\tau )$ is the standard topological space. And $\mathbb{B}$ is the Borel $\sigma $-algebra from this space.

Define set A as:

$A=\{x\in \mathbb{R}:x={q}_{1}\sqrt{{n}_{1}}+{q}_{2}\sqrt{{n}_{2}}\text{for some}{q}_{1},{q}_{2}\in \mathbb{Q},\text{and}{n}_{1},{n}_{2}\in \mathbb{N}\}$

How can I show that the set A belongs to $\mathbb{B}$?

Define set A as:

$A=\{x\in \mathbb{R}:x={q}_{1}\sqrt{{n}_{1}}+{q}_{2}\sqrt{{n}_{2}}\text{for some}{q}_{1},{q}_{2}\in \mathbb{Q},\text{and}{n}_{1},{n}_{2}\in \mathbb{N}\}$

How can I show that the set A belongs to $\mathbb{B}$?