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Can we call $\sqrt{2}+\sqrt{5}$ a number? and if it is a number and we ask about the additive inverse of this number, what is the form of the answer? Which one is more suitable to use? $\sqrt{2}-\sqrt{5}$ or $(\sqrt{2}-\sqrt{5})$

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    What is your definition of number? – 2017-02-15
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    It is a number, specifically an irrational number. What you provided isn't the additive inverse though. -sqrt(2) - sqrt(5) is the additive inverse, as when you add it to the number you gave, you get 0. – 2017-02-15
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    @AliasUser yes you are right it is my mistake sorry, but the point of concentration for me is what should I write it? the number $(-\sqrt{2}-\sqrt{5})$ or $-\sqrt{2}-\sqrt{5}$ or it is the same and there is no difference? – 2017-02-15
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    @Zilliput A number is a mathematical object used to count, measure, and label, and there are different types of numbers. but the point of disagreement is we can call this a number or expression? – 2017-02-15
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    @SamarBahaaeldin Good question. Both are equivalent. Parentheses are used to separate mathematical operations. – 2017-02-15

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Yes, $\sqrt 2 + \sqrt 5$ is considered a "number" by pretty much every mathematician. Specifically, it is an element of a set we call the real numbers. It is not a rational number (a fraction) or an integer (a positive or negative whole number).

The additive inverse of a number is something you add to that number to get $0$ back. So the additive inverse of $\sqrt 2 + \sqrt 5$ is $-(\sqrt 2 + \sqrt 5) = -\sqrt 2 - \sqrt 5$.

You wouldn't normally write $-\sqrt 2 - \sqrt 5$ as $(-\sqrt 2 -\sqrt 5)$, but you could if you want to. Parentheses just help us know in what order we should perform operations like addition or multiplication. They don't change the meaning of the numbers that appear between them.

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    Thanks, for the parentheses, what I mean is when we write a question we should write: find the additive inverse of the number $(\sqrt{2}+\sqrt{5})$ or find the additive inverse of the number $\sqrt{2}+\sqrt{5}$, what is preferred in this case especially? – 2017-02-15
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    @SamarBahaaeldin It doesn't really matter, but we almost always right $\sqrt 2 + \sqrt 5$ (without the parentheses). In this case, they parentheses don't change the meaning of the number, so they are just unnecessary extra symbols. – 2017-02-15
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    Okey, thank you very much :) – 2017-02-15