Recently, I've encountered the following question:

Assume that $n_{1}, \ldots, n_{k}$ are (not necessary distinct) natural numbers. If

$$ (\sum_{i = 1}^{k}\sqrt{n_{i}}) \in \mathbb{N},$$ can we conclude that all $n_{i}$'s are perfect squares? Is there any famous theorem that answer this question? Or, can anyone introduce some references to help me know about this problem?

Thanks in advance.