Can a sum of a finite number of square roots of integers be an integer? If yes can a sum of two square roots of integers be an integer?
The square roots need to be irrational.
Answer
I think this link is a pretty good answer to your question. However, it might be at a level which is too advanced for you, since this is a pretty natural question to ask relatively early on in life, but it takes some significantly more difficult mathematics to prove.
The direct, yes/no answer to the question is "Yes, but only if the numbers inside the square roots were already perfect squares," or equivalently "If you've already done all the simplifying that you can do, then no."
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